Interview with Julian Barbour

0:00 All right, testing, one, two, three, four, five, six. And then I'll say it's the 16th of May, 2000, at about 3.30, and I'm speaking with Julia and Barbara. So you were just saying about the new theory that you've been working on with Neil, that he's a little more gung-ho than you both are grateful for. Yeah, that's right. Neil is, I think, more gung-ho because he's done more of the actual working out of the equations and I think he's got a deeper self-confidence that the equations just are right and that we've got a self-consistent system of equations and there's all this business and it's a constrained dynamical system and the important thing is, are the constraints? Do the propagation equations maintain the fulfilment of the constraints and do the constraints close and bring the proper dirac algebra and all these other questions? Neil has done much more of that than me. Actually a student of his, Brian Kelleher, has also worked on it. In fact, Brian did the first work on checking the closure of the constraints and it seems definitely to work out, and intuitively I can certainly see why it should. I mean intuitively I can understand the theory perfectly. And it seems to work in every respect. I'm losing a little valuable bit of paper there. Close the bag to prevent the recurrence. So, that's one reason for confidence. The other reason is we've really got two results, one of which doesn't come out so strongly at all in the paper that you've seen. What we've got is, first of all, we've got actually a, I would say, a completely new and really rather dramatic interpretation of general relativity itself. It turns out to be, we believe, a geodesic principle in what we call conformal super space with volume.

2:30 And I can explain that later if you like. And it gives a very, very beautiful and we think completely unambiguous dynamical explanation of why Jimmy York's work on the solution of the initial value problems that years ago works. I mean, I don't know how familiar, how are you familiar with Jimmy's work? Yeah, I mean basically the work that Jimmy did and then Neil proved an important theorem for it is the only really useful generic method that exists for finding initial data for general relativity that satisfy the initial value constraints. And if you read the literature, and even what Jimmy himself writes on it, you find that the consensus is that it happens to be some extraordinarily lucky gauge fixing that happens to work. Just one or two people wonder whether it has deeper significance. I mean, Johnny Wheeler, when the work came out, wondered whether it might show that perhaps there's an absolute simultaneity in general relativity after all, which would be an extremely ironic end result, denouement of general relativity. And it has a very specific, Jimmy's work has a very specific structure. It has, first of all, the condition on the Hamiltonian, on the canonical momenta, that the canonical momenta have to be essentially constant. And that's the trick that makes it possible to solve the, it separates the constraints and you can solve them. And then you get, and then the final step is the solution of the Lishnarevich equation, which is a very, which causes a lot of puzzlement to people. why that you have to go from the initial three geometry you've started to a new one via the Lishnarevich equation to complete the process and it was the proof I think it's the existence and uniqueness proof that that Neil contributed to it and that's his contribution to physics all of that has always seemed sort of slightly mysterious. Now what I think is quite clear is that comes out absolutely unambiguously out of our idea formulating a geodesic principle on a configuration space, which is conformal super space,

5:00 where you only have the two degrees of freedom associated with the angles and not the volume, the local volume. In a three geometry, at each point there are three numbers that essentially determine the geometry. Two of them are to do with the angles and one is to do with the scales. and Jimmy already said, Jimmy back 30 years ago under the prompting of Johnny Wheeler had conjectured that the real true degrees of freedom of general relativity were these two conformal degrees of freedom and it was thinking about them that led him to find his method of solving them, but Jimmy and I know this because I had a long interaction with Jimmy I visited him for 6 or 7 weeks in North Carolina in autumn 1902 Jimmy never had any idea of a dynamical derivation from in the configuration space as a geodesic principle he always and you can see this clearly in his papers he always thought of these conformal degrees of freedom as nevertheless propagating within space time just like any other dynamical field. And the picture that Neil and I have developed is quite different. It is that space-time just is not there, there is just conformal super space but it's not, and this is the really key thing, Jimmy was only considering conformal super space but we're saying conformal super space where you still allow the total volume of a closed universe to have physical meaning. Because what you can do is you can make a conformal transformation on a three geometry which is either completely general, which is what Jimmy had in mind, and is what goes into the normal definition of conformal superspace. And let me just interject that the main work on conformal superspace and its mathematical properties have been done by Vince Moncrief and Arthur Fischer. but you can also do conformal transformations which don't change the total volume they leave the total volume so you can put, so to speak, the scale of the geometry wherever you like but you're left with the same total volume

7:30 now that leads you to a configuration space which is just a fraction larger than conformal super space conformal super space has two degrees of freedom per space point so that's an infinite dimensional space and this conformal super space with volume has just that one single extra degree of freedom which is the total physical volume and this seems to be the absolute key insight that we've got that this is what makes it possible to have an expanding universe in general relativity and you can formulate general relativity as a geodesic principle in this theory and moreover when you do that When you look at general relativity as a space-time theory, it looks to be a very beautiful and elegant and natural theory. When you look at it in terms of conformal super space, it looks the most bizarre theory. Because, you know, if local scale has no meaning, then how the hell does total volume come to have any meaning? You know, it's a very bizarre theory when you look at it as a dynamical geodesic theory, as we've done. And what's more, once you've got it in that form, it's absolutely clear how you go to a theory which is much more satisfactory from the point of view of conformal geometry. And that's exactly the new theory we've got. And this new theory, when... In general relativity, if you're doing York's work, you could have a universe which goes from a big bang through maximal expansion to a big crunch. Okay, that's the form there, and it's described by York's method. Now, our new theory is identical to general relativity at maximum expansion, but it differs from it at the big bang and the big crunch, because there's a different term in the equation. There's a very natural gauge in our theory which says that the total volume, gauge which says that there's a nominal total volume of the universe and it always remains exactly conserved. It's a conserved quantity in this gauge and therefore it can never come to a big bang and a big crunch, this theory. It's actually a completely well-behaved geodesic

10:00 principle on a pretty well-behaved space actually. And so you have this situation that here say of the new theory sort of wandering around in a perfectly well-behaved manner. And here's GR coming out of a big bang and going into a big crunch, and up here it's literally indistinguishable from our theory. But it's up here where the solar system tests and the binary pulsar tests have been made. So it looks to us that they should match. but we and Neil, I mean this is where we're guessing at this stage because we really haven't done the equation I said to Neil, what about the nucleosynthesis results and he thought well, maybe it'll be alright there still even too because that's still of course very strong support for the Big Bang but you get a very interesting philosophical I mean it's potentially extraordinarily pleasing from the philosophical point of view because all that can happen in this theory a state of maximum uniformity and and go to states which are ever more irregular and and in fact if this if the new theory is right the big bang will be nothing about an explosion in the past and and and an expansion it will just be about starting from utter blandness and going to ever more interesting structure now in current cosmology you have two quite and things happen. You have the expansion of the universe and you have the growing complexity of the universe what you're part of, what you're observing you know and there's no earthly reason why they should be correlated and in fact Roger Penrose is always saying pointing out that to explain the currently observed universe you have to assume this phenomenally highly uniform state at the start but this is a necessity in our theory So from that point of view, it looks really extraordinarily attractive. Then there's another technical thing which is potentially hugely important. All the work on canonical quantum gravity is absolutely bedeviled by two things. First of all, the definition of time.

12:30 And secondly, the fact that there's a kinetic energy in canonical quantum gravity defined by the Wheeler-DeWitt equation, which is not positive definite. You have the energy associated with the expansion of the universe has the opposite sign to the energy associated with the change of shape. And those two facts, the difficulty of defining a unique time the kinetic energy have been two of the really major problems that have bedeviled canonical quantum gravity for four decades now. Now we just deal with that problem absolutely perfectly because the universe can't expand so that opposite sign that's associated with expansion just completely disappears so we have a positive definite kinetic energy. So that's a huge and that's that that makes the mathematical proofs of existence and all this stuff hugely easier. And secondly, there is a there is a there is a well defined notion of absolute simultaneity as well. So Johnny Wheeler's conjecture 30 years ago that York's work might ultimately overthrow general relativity from within itself, we increasingly feel is correct. So I mean, it's all hugely exciting as you can see. There's one more point too, general relativity is also bedeviled by the fact that you can have hugely many different spatial topologies and so you have a vast range of possible solutions. Now a key thing in, and this is because, and this goes back to the the fact that the kinetic energy of general relativity is not positive definite because it can become negative and at the same time the scalar curvature can become negative and it's okay. Either they're both positive or they're both negative and so they can swap you see. But now in our theory the kinetic energy has got to be positive definite and And this means that the scalar curvature has got to be positive definite everywhere. And this is an extremely strong restriction on possible topologies. S3, which is the beautiful simple one, is the first one for which it'll work.

15:00 And then there's a relatively small class that are related to S3 by some jiggery-pokery. I don't know what it is. That's my understanding of it anyway. So again, you see, we would get a beautiful, I think we've got a very good chance to get a beautifully unique cosmology. And it will be wonderful, really, because the two great cosmological models in the history of thought were Aristotle's closed universe and Einstein's 1917 closed universe. And now we'll have one, too, I believe, spatially closed. And this one will be different from the other ones in that there will be, classically at least, there will be evolution in it. And it will be evolution in which just structure is what is emerging, which is philosophically most, you know, most appealing. So naturally we're excited. So I hope there isn't a flaw in the mathematics. But I mean, and even if nature doesn't agree with us, I think the theory is very pleasing in its own, you know, potentially very pleasing in its own right. and for me it's very exciting too because in fact Bertotti and I could have created this theory 20 years ago we kept on saying we should take scale out of physics and we never got round to doing it and our method actually when I finally got round to doing it I saw that there was an absolutely straightforward way to do it in fact it's only just 15-16 months ago I finally cracked how to do it in particle mechanics mechanics the key insight was what to do to get a theory and I've got actually a very interesting theory which I haven't published at all yet which is a generalization of Newtonian gravity which is scale free and that that was exactly the insight that I needed and I got that in I got that theory in the middle of February last year and by huge good fortune Trinity College Dublin had asked me to come over to talk about the non-existence of time and back in 92 Jimmy York had said to me Julian, the person you should go and work with is Neil he's by far the best student I ever had he's the man who will help you so I've been sort of angling to catch Neil for quite some time and I'd visited him six months before that

17:30 over to Cork, to Cove, actually, to visit friends of my daughter. Well, she came with us. So I took the opportunity to go and see Neil then. And we had a useful exchange then, but Neil was sceptical then, and I hadn't got this new idea. So, I mean, it was just wonderful. So I phoned up Neil, and I said, Look, I'm speaking in Trinity on Wednesday. Any chance of coming to see you? And he said, Yes, yes, yes. So I went down on the Monday, and we talked all of Tuesday and Wednesday morning. And I said to him, I can tell you exactly what you need to do. You've got to introduce a conformal variation, a best matching conformal variation. And he immediately could see you do that. So we got very excited about that. And I went off. And after I'd gone off to America and was turning around, Neil realized that if you do that, then you're automatically forced to do a second thing, which we call the second conformal variation. And that doesn't exist in the original work that I did with Bruno, because of technical reasons but it's forced upon us when you get a conformal work and what's so absolutely beautiful is is is well first of all that that neil and i have each put in a key element there's two key elements in the theory one came from me one came from neil yes uh and neil had worked for an immense amount of time on on some conjecture i forget what it is you'll have to ask neil about that so he was very familiar with this this is why he understood it had to be my condition leads to Jimmy York's condition on the canonical momentum, that it must be constant, or in the new theory that the canonical momentum has a vanishing trace. It's the trace of the canonical momentum must be constant in Jimmy's work, and in our work, in the new theory, it must be exactly zero. But it's my condition, my half of the thing that leads to that, And Niels leads to the beautiful explanation of the Lishnarevich equation, why you have to have the Lishnarevich equation, which is just, you know, it's just fantastic, really. And so, again, if nothing crops up, and I just can't see where it can crop up now, honestly. You see, I'm fairly gung-ho, too. it's showing that there is a there's a deep dynamical principle at work and it's actually

20:00 if we're right it's the end of the relativity principle definitely because one of the ways it's very interesting I've done a lot of work on the formulations of the relativity principle but basically Einstein's position is is there absolutely does not exist any frame of reference in which the laws of nature take on a totally distinguished simple form. They are all absolutely equal for it. And that is true of general relativity when you formulate it as a space-time theory. What we have shown, I believe, beyond any shadow of doubt, is that actually within general relativity when you look at it as a dynamical theory that is an extremely well-defined, uniquely defined frame of reference, and that's Jimmy York's one. Because we've got a... It is not a gauge-fixing condition, what Jimmy has done. It is a reflection of a deep, physical, dynamical property. And the same goes for the conformal gravity. So I'll stick my neck out and say... I would say I now do believe this is actually the end of the relativity principle. And Neil and I, we keep going through the arguments, we keep looking at the equations and we just can't see where there's anything wrong in the arguments. What has to be done is absolutely clear. Bertotti and I set out this absolutely clear idea of best matching in a relative configuration space. The prescription is absolutely clear what you have to do. we did it for particle mechanics we did it and sort of got something very like general relativity but general relativity remains a very funny one and now we see the reason why general relativity looks so funny is that Betot and I just didn't go that one step further and explicitly take local scale out of physics and once you do that everything is transparent, the whole thing and the program is so so clear you see the and what it's also showing is that I mean what everybody agrees is that gravity seems to be described by a field with spin 2. Now there's always been a mystery to me about this question of the spin 2 and

22:30 for that matter the spin 1 of the Maxwell field because that is reached by the condition that the, that you have an irreducible representation of the three-dimensional rotation group. The condition, as far as I can see, the condition that determines all the physical fields that we know of owes much more to the condition of irreducibility with respect to the three-dimensional rotation group than it does to four-dimensional symmetry. It's very striking. I know this from my PhD in Cologne, which was on the flat space approach to general relativity, where, I mean, essentially what I showed there, which other people have realised before, but I think I showed it more clearly than anybody else and brought out the importance of it, I think, is that it's the condition of irreducibility with respect to the three-dimensional rotation group that counts. And that is what, that's what actually makes gravity have two degrees of freedom per space point. Now it seems to me a complete fluke. It just so happens that if you have a four-dimensional generally covariant metric theory, it turns out that the gravitational field will have only two degrees of freedom. But you also get exactly the same result if you ask for a three-dimensional theory that has got conformal invariance. If you ask for a conformal theory, you also arrive at two. And I think it's just one huge, colossal historical accident that that fact of two degrees of freedom for space point happened to turn up through the four-dimensional approach, generally covariant four-dimensional approach, when it could just as easily have turned up as the way we've now found it, as a conformally invariant, a three-dimensional conformally invariant and you can moreover see why these two theories match because in the conformal approach there's a whole range of theories that are possible which satisfy the conformal invariance requirement but there's just one of them which satisfies the space-time requirement so that you can say that the space-time form of the theory this very odd space-time form of the theory historical accident that Einstein because of Minkowski saying there is a space-time and Einstein

25:00 working on it and then Grossman coming and getting all the thing there, you see. So this is potentially very intriguing, really. It's very... You see, it also illuminates a lot of... There's a lot of real puzzles about the canonical approach. I've just come back from working with Neil both reading these very influential papers, well this very influential work that was done first by Dirac on understanding how fields would propagate in a four-dimensional space-time if you go from one surface to another arbitrary one. This is the many-fingered approach that actually started in quantum electrodynamics, Tomanago. That's what Tomanago got his Nobel Prize for as far as I know. And then that approach of Dirac was taken further in two beautiful papers, one by Claudio Teitelboim and then a joint paper by Sergio Hochmann, Carol Kuchasch and Claudio Teitelboim, in which they derived general relativity as a representation of a group, in scare quotes, group of deformations of four-dimensional space-time. And it's very interesting when you read those papers, you see that on the one hand there's an extraordinarily clear heuristic principle at work, but on the other hand that it's a mathematically very funny one and isn't quite right. and that's why they haven't got a proper group. And what's so particularly mysterious about that is that you start off from the four-dimensional thing but all the equations you get show no trace of the four-dimensionality when you've got it. All the Dirac algebra, the whole Dirac algebra, There is no explicit trace of the four-dimensional metric. It just completely disappears from it. And it's a hidden symmetry. The fact that it's a space-time theory is a really hidden symmetry. And I would bet a million pounds that if the closing relations had been found independently by some argument,

27:30 nobody in heaven would have dreamed that it was a four-dimensional space-time theory because it's absolutely not there in the equations. You want to look at the Hochmann-Kuchasch-Teitelbaum paper and look at the structure of the closing relations. There's no trace of four-dimensionality in them. You would never have dreamt it. completely impossible for anyone to have seen it from those equations. Nobody would have realized it. And in fact, I think the opposite thing is happening the other way around, that nobody's realized that actually it's a three-dimensional conformally invariant theory. Because it was found that way. That's what it is. So, I mean, it's potentially big. Yeah, it's very interesting. It's damned interesting. It's been terrific fun, too. Neil is great to work with. It's lovely going over to Cork. Shall we take a little break while I finish my tea and things? I don't know if you want to switch off for a moment. You can leave it on if you like, but I'll be munching. Sure, yeah. I'll have a sit in my bed. I think I've given you the complete picture of the thing. I'd have thought that's not a bad summary of everything that's going on. Now, as to what we're doing, well, first of all, Neil wrote, I thought, this really excellent paper, four pages. I thought it was a masterpiece of condensation and precision, and we submitted to physical review letters back in the summer in the confident assumption that it would be refereed by Carol Kukash and Jimmy York and would be published and we would be, dare I say it, world famous before Christmas. Our first referee, we got neither of them. Carol had had a row with physical review letters and Jimmy's not well, sadly. The first referee we got was just obviously an idiot. I don't think he'd ever heard of the ADM formalism. He complained of a curious three-dimensional formalism, I ask him.

30:00 So, and this dragged on and dragged on and dragged on. So then we said we wanted to have another referee look at it. So they actually sent it to two more referees. We got another referee who was just as bad as the first. And then we got a third referee who was much more reasonable. I mean you can have a look at the reports Neil's got them, probably better to get them from Neil than from me because I probably put them somewhere where I can't find them the third referee actually brought home to me his comments were much more reasonable and you can understand what he was having or she was having differently was that well basically people don't know and understand the ADM formalism it's just not widely enough known I think among people And we circulated it to about six or seven friends. Basically, Neil was disappointed with the response of his friends, Bobby Bike. He said he didn't want to know anything about it. My friends were much more positive. Lee Smolin said, this is very interesting, but for goodness sake, as soon as you can, write a really long discursive paper on it because people just don't know about Jacobi's principle, about byline, sharp, wheeler, they just don't know about it. And it's, I mean, recently I was talking to Lee about those of us who were interested in the structure of general relativity as a dynamical theory, and he said, all five of us, you mean, he said. Well, that's a bit of an exaggeration, but it sort of, it brought it home to me, and also it was very interesting, I spoke at the Royal Astronomical Society meeting. I don't know if you heard it. Were you at that meeting when I spoke for Herman Bond's 80th birthday in the autumn? Personally, I couldn't... Well, I spoke at that. Neil came over for it. We felt the presentation went very well. Nil response from the... No, there was one intelligent question from the audience. And then the next night I was lying in bed and it suddenly occurred to me that Iraq had started all this three-dimensional approach and not a single person of any stature in Britain had followed it up. The ADM stuff is done, practiced in America. Hawking knows about it and uses it, but has not made any significant contribution to the theory itself

32:30 and neither of any of his students, although Jonathan Halliwell knows the formalism and has worked with it. but they've not worked on the formalism itself. And there isn't a soul in this country that I can think of that knows about it. So, I mean, I think there's a major... I mean, this is, if you want, a real paradigm matter that there's... The idea of space-time has just got so deeply rooted now that, you know, anybody who questioned it is almost certainly a nutcase or anti-Semitic or something like that. I mean, let me tell you something about Carol Kuchasch, and this is sort of off. Maybe you would ask Carol for his permission. I went to, after I'd been to the community, I went to work with Carol for four months in Salt Lake City. And this was long before this conformal stuff came out. about the basis of general relativity and whether the Machian approach that Bruno and I had developed was the more important one or whether the space-time one was and so forth. And we also got on to the tension that has always existed between the space-time approach and the dynamical approach, which is characterised by this curious thing Kugas-Teitelbaum paper Carol at one stage suddenly looked at me and he said, Julian it may be I've spent my whole life doing the wrong thing I said, what do you mean, Carol? He said working on the canonical approach so then I said come on, Carol what do you really believe in? What's your deepest belief? And he started with the opening words of Minkowski's famous paper And from now on, space and time will cease to exist as separate new entities and will be fused into one thing like that. Which just isn't really compatible with the canonical approach. There's always been a deep tension there. And I think, in a way, Carol has never managed to resolve that. And it's the reason why he's done an immense amount of extremely good work.

35:00 he's a very disappointed person he's stopped working on the canonical approach he's doing consistent histories I'm told I'll be seeing him soon and I saw him now I saw him last 13 months ago after I'd seen Neil and we got the thing going but before we knew about the second conformal transformation, the Neil's contribution and I remember very much, we sat at breakfast in his home in Salt Lake City And he said to me, Julian, there has always been a problem with your Machian approach. You just can't get the facts of relativity out of it. You know, relativity does not appear naturally out of your Machian approach. And I said, Carol, I think you've been right up to now, but I think now the matter is set. And it's gone against relativity. And so we'll see whether I've vindicated or not. my feeling so I think from the point of view of sort of paradigm shifts and things the thing that really strikes me is that immense magic of the Minkowski paper it's just and the Einstein definition of simultaneity and what he achieved with it and then followed by the Minkowski paper And then the miracle of getting the perihelion advance for Mercury out of general covariance. Dazzled people so much. There's two things they missed. First of all, all this complete and utter confusion about general covariance, which Einstein admitted after the event. All the Kretschmann stuff, which John Norton has. And then there's another fact. I don't know, have you read my book The End of Time? The other thing that I think is hugely significant is that Einstein actually had, I think, remarkably little idea of what his theory really was, and he did not actually create it himself. What he got was the idea of a space-time theory with four-dimensional curvature, that it should be generally covariant. And then in my book I say, he hurried to a shop in Zurich run by his friend, a gross man called mathematics,

37:30 and took a device off the shelf, which is called the Ricci tensor, twiddled a couple of knobs, and it worked. I mean, the perihelion advance came out. And then he never asked himself what was going on, which is completely different from what Newton did. Newton literally created his complete theory, ab initio, from the barest hints that he got from Descartes. He did it without using Galileo's stuff. He did it all by himself, combining it with Kepler's observational results. And Newton created the mathematics and all the physical concepts and the whole theory. And from the word go, knew what it was. If you look in Einstein's papers in 1916-17, particularly, for example, his formulation of the whole argument, you see that he has no clue what is really happening in his theory he is mistaking his theory for poisson's equation when it's really a constrained wave equation and he died not realizing that there was anything wrong with that which is you know an extraordinary irony and i think he could do it i mean my my my feeling is that that einstein was doing about six or seven different things at once when he created general relativity and he did five of them with just sort of fantastic panache and that was enough to get him through to the results he needed and so he never bothered about the thing which was the real stimulus, I mean the real stimulus was actually the Mach's principle but he never asked himself how to do it it's amazing how he didn't he never really read Mach properly I'm sure it's all going to come out in the volume two of my absolute irrelative motion so I think this sort of is the explanation for the thing I think if that's the way it works out but I mean, alright, Neil and I may have terribly red faces as red as the shirts of Manchester United but we can't see it at the moment so it was so it was working on formal version of Newtonian theory that gave you the that gave me the key insight you see I've been

40:00 I mean I don't know if you know the story of my book Absolute or Relative Motion you know the book the volume one now I originally had a contract which I signed in the autumn of 84 with Cambridge University Press to write a book of 400 pages covering the stuff from Newton to Einstein and including the work that Bertotti and I had done. And then, just before I started, I suddenly said to myself, I wonder why Newton said what he said. Hadn't I better look at Galileo? And then that led to this complete book, which I had no plan of writing. It was a marvellous experience writing that book. stuff and this huge book of nearly 800 pages came out of it uh and then my editor was very nervous he said well julian please get on and bring out volume two as soon as you can because it's not going to be easy to sell a volume that big uh when when it's not even the two volumes yet you know and uh well first of all lee smolin threw a spanner in the works by saying which i was already aware of was that there were a lot of implications of the work that Bruno and I had the machine work that Bruno and I had done for the problems of quantum gravity and you I don't know if you've noticed that Gordon Bellot has recently published a paper called relationalism rehabilitated and anyway that group around John Ehrman and also the group in Oxford they are really now seeing that the conceptual problems of canonical quantum gravity are really just the old absolute relative motion debate in a modern guise and in fact i think i can take the credit for that i mean it um the first paper where that was clearly stated is one by myself in um a book put out by penrose and isham in 1986 when i i spoke in 1984 at a conference in oxford where and and that's that's sort of worth looking at and i mean it sort of all seeped through from me via lee smolin via carlo revelli i mean this um bellot and earman out in the Calendar Hug It volume on physics and philosophy at the Planck length, which

42:30 is due out fairly soon. And they talk a lot about the problems and say, yes, this is a revival of the absolute relative debate, the substantivalism versus relationalism debate. And as Oliver Pooley in Oxford says there, their paradigmatic relationalist is Carlo Rovelli. And their sort of man-torn in not quite knowing where he is is Carol Kukash. They thank both of them for their tutelage. But it's a huge paper. And my own stuff actually there only gets a footnote or two. But Bellot actually gives my, in an earlier paper, gives me quite a lot of sort of prominence in the thing there. But, I mean, Rovelli got it through Smolin and between you and me. Lee is wonderful. He keeps saying that I've taught them all about these issues, but they don't understand what I'm saying even yet. There's still none of them. None of them. Neil does now and Bruno does. fair topic. And so does Oliver Pooley and Simon Saunders in Oxford. The Oxford group have really understood what I'm on about and what's the important stuff because I talk to them a lot. But dear old Carlo and even Lee who's been a marvellous friend of me. I don't think Lee still really understands what I've done and what I'm saying. He's so busy doing other things. He's got this beautiful wife now. And all this is to do with the whole argument and what's the significance of the whole argument and nobody's... The whole argument and Einstein's recognition of his mistake is only the beginning of the story. And I've got a paper which is coming out also in the Huggett calendar volume where I think it's showing exactly what is the real true significance of the whole argument because it actually is, the whole argument that is presented is as if the problem is different descriptions of one four-dimensional universe and are they in some senses physically different or are they for there. Now that's quite true and it was when Einstein saw

45:00 that the different representations are all just the same space so it doesn't matter, he was quite right in that And that showed that his argument against general covariance was wrong. Then he could see that his theory could and should be generally covariant. And I heard John Stachel talk about this in Stockholm at the GRG meeting in 1986. And at the end of the talk, I got up and said, I mean, it's obvious to me that what Einstein had done was actually rediscover Leibniz's principle of the identity of indiscernibles. And that's clearly what it is. And that's how Norton and Ehrman interpret it. this expression, whatever it is, Leibniz in discernibility or something, or Leibniz equivalence, which I think anyway they've got from my 82 paper in the British Journal for the Philosophy of Science. I mean, John Ehrman too, I must say John Ehrman was the first philosopher of science who really started to see that Bertotti and I had done something, but the sad thing is that he only appreciated the significance of our first paper, which is actually much less significant than the second paper and he did I would say completely miss the significance of the second paper but the I think the sort of the so anyway the sort of what comes what I make clear in the in I think already in the 82 paper but certainly now in this paper that's coming out in in calendar hug it is that the four-dimensional business is utterly trivial and in fact theoretical physicists who know their stuff can't think what all these philosophers are wiffling and waffling on about all the time anyway because to them it's totally obvious what the answer is the real issue is if you are dealing with three-dimensional things that are different and you haven't got an absolute space in which you can embed them how do you match one point of this space to another point on another point of that space and you have and that's actually the that's actually the whole argument in a different thing where you're forced to confront that issue and and and the best matching technique that bertotti and i developed and now neil and i have taken further is actually the method that is used to resolve that and it's something quite different from the normal way of things and it's actually a It's difficult to explain it on paper,

47:30 but when the Hug It calendar volume comes out, you want to have a look at that paper of mine because it sets out what it is. This is the key thing that nobody properly has understood. Well, Neil has understood it now, and so has Oliver Pooley. But this is what's really behind all the Norton saga of the seven decades of confusion. I mean everybody is arguing what is the significance of general covariance they're not asking the correct question the correct question is what is the precise manner in which general relativity differs from any other physical theory that existed before it and when you look at it that way you see that it's because it solves this problem of how you put together three-dimensional things and this is intimately related to the dilemma presents to you and it's it's all laid out it's it's absolutely clear in my mind that that's what it is and they've been asking the wrong question and that's why there's been this endless confusion about general covariance because every theory must be generally covariant the question is what specific structure does any theory have because any theory has got to be generally covariant but the question is what's the specific structure and that's where the key thing comes in And that's where the idea of best matching is so all important and so on. So, I mean, you've got it on tape now and you'll have to do the background work of reading it up and so forth there. But I feel I'd risk going before a firing squad on that issue there. I know that's the answer. And I'm almost as confident about going before a firing squad for the stuff with Neil now, too. I mean whether nature agrees with us that's quite a different matter but the inner logic of the theory and the mathematics I think it's right I think it's right and Neil is I say Neil is very gung-ho let's see if we get red faces I guess the other thing then of course is the sort of historical sociological aspect of it that in a sense what you're trying to do is to precipitate a paradigm shift in which people stop looking at it as a universe as a four dimensional thing and start looking at it

50:00 as a three dimensional conformal thing and I suppose in that sense the sort of reception that you've that you maybe have had so far I get the impression from talking to you and which has been sort of in many cases is reflective of that that people are not quite grasping what you're saying yes that's perhaps fair enough because there's nowhere where I've said it as forcefully as I've just said it to you because up to now we haven't been really confident and Carol was absolutely right the crucial step was making the conformal I mean I was in my bones that the three-dimensional thing was was extremely important and had been seriously underestimated but it's you should read my end of time in this because in the end of time I'd actually when I finished it Neil and I'd actually already when it was going to proof we actually already had the key results but I didn't dare to put it in the book because it was much too new and so forth but in the book when I wrote it before I got the results with niam i mean the central dilemma in the middle of the book is is is it three-dimensional or is it four-dimensional is most important and and i in the at the level of the classical theory i agree with carol and say the four-dimensional is more important but then i say three-dimensional part is so striking and when you come to the problems of the quantum theory it seems to me that in the quantum theory, only the three-dimensional one will work. And that just tips the balance for the three-dimensionality, which is, by the way, exactly the position that Dirac came to back in. You should read what I say at the start of my book about the one sentence from Dirac. By the way, I can let you have a copy. I'll give you a copy there. I've got some answers. Dirac was very surprised. I mean, Dirac saw clearly this very strange more sensible as a three-dimensional theory when you treat it dynamically. And he said on the basis of this result, I'm inclined to believe that four-dimensional symmetry is not a fundamental property of the world. And I keep on saying this to Carol. And Carol said, Julian, you're misinterpreting Dirac, but I know bloody well I'm not. Carol just doesn't want to see the truth.

52:30 By the way, Carol is a hugely good friend of mine, So there's no animosity at all in that remark. It's been a really good argument between friends. But if you go back to that early literature on the canonical stuff of the late 50s, early 60s, you'll see that Dirac and Johnny Wheeler were coming out with really strong conjectures and really were giving out strong hints then that there was something wrong with the relativity principle. but it wasn't quite right at its heart. And if I do succeed in bringing her around a paradigm shift, it will be because of my reaction to Dirac's remark, which was that I thought that the newspaper article I'd read went on to say, and Dirac therefore thinks that we should... It was a newspaper article in Germany, and therefore Dirac thinks we should actually think about what time is. But I went to the Trouble a few years ago, actually fishing out the article and looking at it and it isn't there that idea occurred to me that i should and i just had a fantastic 10 days when i well i i did go manic actually thinking about all these things and and suddenly came to the very deep conviction that time doesn't really exist change is primary and and that the whole of physics needed to be recast on on a new timeless basis i've set this out in the end of time and And my feeling is this work with neolysis has actually completed the job. I think it is the end of that task that I set myself 37 years ago. It looks to me like it. It's worked out exactly. I mean, I got the key notion of the relative configuration space in about 1971. blackboard in the kitchen here and i you're in the book you'll read i wrote up a sentence on the blackboard the history of the universe is a continuous curve in its relative configuration space and i said to my wife that's important um neil and i have now shown that it is true if the configuration space is conformal super space uh in either form either it's gr which i out now or it's or it's our conformal one and of course this is not the end of the story because

55:00 we've still got to unify forces and things you know i mean you know i don't think this is not the end of the story but i think it's i think it's a it's definitely got the potential to be a very significant step i i would i i i think i think i've won the argument with carol i really do what do you think would be do you have a feeling or a suspicion as to what would be implications of the new theory which would be most likely cause people to as it were sit up and take notice to stop saying well I don't really understand that so there's no point in looking at it right now well our plan is the plan is at the moment is that Neil's going to work on a longer technical paper and instead of writing a long discursive paper and putting it on the bulletin board Neil and I have now decided that I should write a slim volume and it's going to be called best matching conformal gravity an alternative to general relativity and I'm hoping to write it in the next two or three months I think I can everything is now pretty well crystal clear to both of us um i'm going to propose to my editor at oxford university press in the states who brought out my end of time in the states to to to publish the book um there's already a lot of interest in in actually the neil and i wondered whether anybody had noticed our paper that we put on the bulletin board uh back in november but i got phoned up by a frenchman to ask me to be on the... He's done a paper on Mach's principle for his PhD and he's asked me to be on his jury. And he's read it and he said there's some very interesting connections. He's been working on topological field theories in four dimensions and he says there's a very interesting connection precisely with what Neil and I have done and with the dilaton that comes in string theory. And I've actually suspected for a long time there is a connection with the dilaton in... has a chance actually to bear on the dilaton problem in string theory, but I don't know enough about it really to say on that. My hope is that the end of time has given me so much exposure now. I mean, it's being very widely read. It's getting a lot of discussion.

57:30 I mean, newspaper articles are now quite often appearing and I'm sort of regularly being coupled with Hawking. I mean, after all, coming out with a clearly argued case that time does not exist at all does make people sit up and think, you know. I think the inner coherence of the theory ought to win people over quite quickly to take it seriously and then work on the elaboration of it is our sincere hope. I mean, let me just be ever so slightly naughty and quote from the Gospels. He that is out of the truth will hear my voice. That theory has got an inner coherence, which anybody who studies it intentively... Intentively? Have I got that right word? intently one of the words anyway one of the two you cannot fail to see the inner coherence of this new theory um i think neil and i are a very long way still neil neil is sure it'll come out right i'm not quite so sure that it will i think it's still a lot of work to show that we would say recover the binary pulsar results and the solar system tests to the accuracy which we believe we haven't yet fully we haven't yet worked out the the coupling to matter which is essential um and there are problems with that it'll work for massless fields you know there's this there's a lot of a lot of hard technical work there i mean neil talks about 10 years hard work on this theory and i would say that's probably probably true um and then there's all the question of of how it might be quantized and so forth i mean that's all very exciting too potentially but if i'm really optimistic i would say that the whole i mean i've been always far too optimistic in how quickly this work would get recognized that i've been trying to do now for 37 years i would hope before the end of this year the whole physics community theoretical physics community ought to be talking about our paper that's my judgment on on what ought to happen And that's what Neil thinks too.

1:00:00 We'll see, we'll see. It'll be very interesting. So, to get a more detailed history, did you do doctor work in Cologne? yeah I mean I had this I was going to do I did maths at Cambridge then I took a year out to learn languages Russian and German in Munich and then I started a PhD in astrophysics in Munich had to do more physics to do that and then got thoroughly hooked on basic issues in physics particularly I started reading Hermann Weill space, time and matter and then just purely by chance in October 63 I read this newspaper article Iraq's work and it just had this fantastic impact on me. So then after a year of hesitation during which I actually got married, I gave up the idea of doing the PhD in astrophysics and went to Cologne where Peter Mittelstadt gave me this thesis to do on, I wanted to do it then on Mars Principle but Peter said no look you won't get a job in a university if you work on principle do something a bit safer so i did this work on on the flat space approach to general relativity which was good training for me because i learned quite a bit of important notions about irreducible representations and stuff like that um but i i'd have said it was a fairly ordinary thesis there wasn't anything very much much in it and and then i when i'd finished the jobs, it was ironic if I'd applied for a job at one of the outside Oxbridge in this country back in about 64 I only got a second in maths at Cambridge and a pretty middling one at that and I didn't do part three I was told I would almost certainly get a job at a provincial university if I wanted it but by 68 when I finished my thesis the jobs had dried up because of the Vietnam War which meant that the Americans were not taking so many people from Britain it was much harder to get in and then I there was still a chance and I went and had a very useful discussion

1:02:30 with Felix Pirani at King's College I hadn't actually I hadn't taken to working in an institute in Germany to be quite honestly I think I'd take after my father who was an independent scholar for a long long time Felix said to me if you think you can turn out one or two good research papers a year do the lecturing and administration then a university job is for you if you don't think you can do that think again and I said no I can't do two research papers a year now you're meant to do four or five it's absolute madness in my opinion and luckily i'd started i'd learned russian and i'd started already when i was doing my phd i'd been doing some russian translation for an american publisher this cover-to-cover translation of the journals and realized i could do it quite quickly and earn quite a lot of money with it and and then by extraordinary fortune i'd already bought this place i mean that's you can read all about that in the book um so i said hell i'm going to go independent and i'll just publish answers when I've got something worth doing and and the really key thing was the very first the first paper I got published in 74 and I mean I had a small completely unimportant joint paper with Mittelstedt in the Zeitschrift for Physique in 1967 but or 68 but my first paper was in 1974 in Nature, and it was a fantastic piece of luck, because a young Italian, it's a very nice story, Francesco Padula, at the age of 16 or 17, he'd been introduced to Newtonian mechanics, and suddenly said to himself, there's something wrong here, and he'd come up with Marx's objection to it. Anyway, he went away and did his military service and thought about it and went to university and then he he came up with a theory which was essentially the the absolute space part of the theory without the time idea the absolute space part of the theory that i published in nature he went to his professor in in milan and said i've got this theory um the man said look i'm awfully sorry i can't make anything of this why don't you go and see bruno bertotti in pavia so bruno looked at it and said no this is good this should be published and they we're going to do a paper together when Sunday Bruno found my paper in nature. So then Bruno wrote to me and then we collaborated and then we had this fantastic collaboration

1:05:00 for about six or seven years. And that really laid all the foundations of the thing. We had this, our first theory we later discovered. I could never understand that it hadn't been discovered before us. And then quite recently, this is all in the, you know, I edited this volume at Tübingen Conference. I'll show it you upstairs if you want to know it. It eventually turned out that our theory had already been discovered several times before. The first paper we did, most dramatically by Schrödinger in 1925, his last paper before he created quantum mechanics, wave mechanics. There's quite an interesting prehistory to that. But Bruno and I could see clearly that that theory wouldn't work, although it was manifestly Machian. It predicted anisotropic inertia, and that's just completely so then we looked for an alternative idea and then I came up with an idea which I'd actually already had back in 1972 because I discussed it with Charlie Misner in Oxford in 1972 which is this best matching idea of trying to see when two things are as close to congruence as possible and that's the key thing and Bruno immediately saw the potential of this and worked out the mathematical techniques of doing it and that's really the co-thing in this work. There's the idea of a relative configuration space and the idea of defining a geodesic principle on it by best matching. So it's just two very simple clear crystal clear ideas and it's just a matter of sitting down and doing the work and I've never been very good at equations and and so you know Bruno, first Bruno and then Neil were the absolute ideal collaborators for me. and Carol Kuhash has been wonderful in terms of giving me technical understanding and so on and Lee has been marvellous in giving me encouragement to keep going and saying look what you're doing is important, this is very relevant to things so that's really the story of my life to be quite honest And it's quite funny, actually, I told my family when we settled here in 1968, I said, you know, I'm starting a life's work, this is going to take me 30 years to do. Spot on. It hasn't ended yet, I don't think.

1:07:30 I mean, it's wonderful now because through the book I'm meeting all sorts of interesting people. it was i i don't regret one minute coming out here and living a bit like a hermit but i was i was terribly reliant on just two or three people i mean it was bertotti kukash and smolin really for a long long time were the only people i was really seriously interacting with and it was it was too small a base um the really decisive one was actually going to work with jimmy york wonderfully positive person and he's very very interesting person Jimmy very and I think I mean I said to Jimmy I met Jimmy in Salt Lake City when I went to work with Carol in 1980 and then I met him again in 1991 when we went to this conference on time asymmetry in Rome and he and I arrived at the airport at the same time and I and I said do you remember me Jimmy and he And I said, Jimmy, I'd like some time to come and talk to you about your work because I personally feel it's the culmination of classical dynamics. Now, of course, please, Jimmy, no end. But I think it's right. And I think Neil and I have proved it too. But Jimmy is very positive. and after I'd interacted when I was with him he said to me Julian it's not good enough to do good work you must make sure people know about it and that suddenly struck me and then you know that's what's been behind that was actually what was behind me deciding to write The End of Time and try and break out to a much wider audience and then force people in the field to take me seriously and this is actually happening i i you know it's it's exceeded beyond my expectations i think in this way i mean it's still early days but i'm getting a lot of feedback there's a lot of people out there reading it you know it's a real eye-opener to them the idea of the relative configuration space and things like that you know that's it's it's it's having its effect. So I believe this should be a good springboard for the reception of

1:10:00 Neil's and my work when we manage to get out of the longest cursive account of it. One of the problems, a crucial part of it is using Jacobi's principle. I don't know if you're familiar with Jacobi's principle. Jacobi's principle is the theory which tells you the orbit of a conservative dynamical system without telling you how fast it's going in the orbit it's it it's it's actually in the two in the two body problem it's actually the way you find the kepler you solve the kepler problem you find the orbit first that it's an ellipse and then you use the energy theorem to find how fast it's going around it and the in the general n-body case what you get is if you have one fixed value of the energy you have a geodesic principle on the configuration space and in fact what I mean a key part of the story was that I found I found this method completely I do nothing whatever about Jacobi's principle and I found this method in my 1974 paper and and it is the basis of all the work on this approach including what I'm doing with Neil now Jacobi's principle and then Bruno and I when we did the best matching started working seriously on the best-matching idea in about 1979, and we'd got a form of a theory which we thought was going to be a rival to general relativity. It was variable geometry, but it was only three geometry, it wasn't conformal three geometry. And I met Carol, there was a big conference in Oxford, the second Oxford quantum gravity conference in April in 1980 I think it was in Oxford and I met Carol and I said because I'd met Carol already eight years before and I said Carol look, Bruno and I have got something we think is really interesting, can I come and talk to you about it and discuss it with you and so forth and he said yeah come out to Salt Lake City in the autumn so I did and he looked at the paper and it's quite interesting looked at my early my nature paper and when he looked at my nature paper he said Julian I'm I have some feeling that what you've got here is actually one of the great principles of um of dynamics that nobody studies now I think it's Gauss's principle of least constraint go and have

1:12:30 a look in Cornelius Lanchos's book and see if that's the case so I did and it wasn't so when we got to when i got salt lake city carol looked at the the book again and he said julian i still have that feeling that you'll find this in landshops try again on on the principle of least constraint but also have a look at jacopi's principle and there it was i can remember walking up through the snow and it was october and it was snowing and walking up through the campus in Salt Lake City to the library and looking, and that was Jacobi's Principle. And then that jogged Carol again, and he said, now go and have a look at the paper by Byerline, Sharp and Wheeler. And that's when it came to light that the Byerline, Sharp, Wheeler paper is a formulation of general relativity which looks extraordinarily like Jacobi's Principle. And it's still amazing how few people realise this fact. I believe it's deeply significant, It hardly appears anywhere in the literature except in my papers. And I cannot understand it. Amazingly, Carroll has not worked on it. I keep on saying to him, why don't you do further work on this, Carroll? But he never seems to get around doing it. So that was quite an interesting... That was an absolutely key observation of Carroll's because it took us to the byline Sharp-Wheeler action. and then this was the point of departure for Neil's and my work because essentially Bruno and I had all but found the Byerline Sharp Wheeler. We got three quarters of it. We didn't get the part that deals with the very special properties of time in general relativity. We got everything else exactly right, but not that. and the obvious starting point for the new work with Neil was to take the byline Sharp-Wheeler thing and convert it from being a theory in superspace, which is the space of all three geometries, to a theory in conformal superspace. And the way to do that was just perfectly obvious. I mean, you know, it was settled in... Well, I mean, the first step was settled in the afternoon. I was there the morning. Tuesday and Wednesday morning with Neil and we'd settled that on Wednesday morning what had to be done for the first step

1:15:00 and then it was about another two weeks and Neil had realised that the second thing had to be done as well so it all went from byline Sharp Wheeler so I mean that's the thing and I mean it hadn't been for Carol's observation none of this would have happened it's amazing how things fit together and go on and that's also why my second volume of absolute or relative motion hasn't come out. Because, first of all, Lee got me interested in quantum gravity, and then I got very interested in the interpretation of the Wheeler-DeWitt equation. So that delayed me a whole time. And that led to, in the summer of 1991, I had this idea of time capsules, which plays a central role in my book, The End of Time. So that delayed me. And then I thought, well, now I'll get on to volume two. asked me to organize this conference on mass principle in in in tubing and uh which i think was a great success and it was terrific fun working on the volume of that but it was one hell of other work so that got delayed and then i knew there was one last thing that if i was really going to do this thing properly i had to deal with scale i had to make it conformal you know and and four exactly four years ago it's almost to the day four years ago i finally decided i'd translating I would give it up and take a risk on the size of my pension fund and that then released me to I've been much more active since then this is this has been vital and the first thing I decided to do was to to try and write a popular book so through Lee I got an introduction to the Brockmans this incredible literary agent in New York, and that was set in motion, the contract and so forth. So that was in summer, this all happened in summer 1996. The proposal went into the Brockmans, I think, in July or August. And meanwhile, I said to myself, well, what I must do is finish volume two if I possibly can before the end of time, because I'd rather have the technical stuff And there were two main things I had to do. I had to do a lot of work on how Einstein had come to general relativity. And I did that in the autumn of 96. I spent about six months working on all the Einstein.

1:17:30 I think I looked at every single paper Einstein wrote on relativity and a lot of the correspondence as well, published and unpublished. Very interesting it was too. And that's where all these sort of very interesting insights, I think, into how Einstein had worked had come. all that's actually written up and then I said now there's one more thing I must do which is get scale get that one and then I can write volume two you see and so I was working very intensively and this time three years ago I had one of the key insights which finally led to the thing that was with working with I went to Bertotti again for a week in April 97 and I got very close to cracking the problem then and another person who's been very important in all my work has been Nico Ciulini, Domenico Ciulini who's very interested in fundamental dynamical things and Nico had been very helpful and I'd sort of really made the problem I'd completely clarified the issue with Nico and with Nico's help I'd said the obvious thing to do is try and find a geodesic principle formal super space that that that came in three years ago uh when i was interacting intensively with nico and then meanwhile the pressure was building up to start work on the end of time because um uh you know i'd signed a contract i got some quite useful advanced royalties and so So, in the summer of 97, I finally had, with great regret, I had to put the conformal stuff on one side and started to write the end of time. And then I wrote it and it got a terrific rush at him because OU, Weinfeld and Nicholson wanted to bring it out in the end. Suddenly they asked me if they could bring it out in March of... I'd nearly finished it by... I'd nearly finished the first draft, this time two years ago in 98. I wrote it quite fast and they said we want to bring it out very quickly and so they pushed me and pushed me and I produced a draft which was too technical

1:20:00 and the new editor came in correctly said look this is just too technical you'll have to rewrite it. So I rewrote, I cut quite a bit but I rewrote stuff and that went through to the end of 88 and spring, at the end, it was end of January 99 I'd finished the book and then I immediately set to work on the conformal stuff and had cracked it within, the first step I'd cracked within two weeks was some quite nice email exchanges. I got it all there if you're ever interested in wanting to get all the details. That was in I went over to see my son in Paris on my birthday in February 23rd and went to see Christian, because a lot of this was, a lot of help, I got a lot of help with people working in the three-body problem. Pete Huff at the Institute for Advanced Studies, he had introduced me to him and three of the guys spent ten days in Princeton with him and Douglas Heggie in Edinburgh working on the three-body problem and trying to understand it purely in terms, if you only knew the angles formed by the three bodies what equation would it satisfy that was that was a very important part of the formulation of the thing and anyway so so Douglas Hegey I wanted to have a little I want to organize a little seminar on the three body problem and try and crack it with with x real experts and I asked Douglas Hegey whether he would come in and he said look I'm just too busy with the work I'm doing with Pete Hutt but I can tell you two people you should get hold of one is donald linden bell who i knew anyway and donald has always been actually very supportive of my work and he was the referee of of the second paper with bruno and has followed it very with a lot of interest and he's actually made quite interesting development of the theory the particle one um and he said another person is christian marshall in in paris and as i was just going over there i i went to see marshall and that was all very important because it it it led to a whole insights there, which is still not elaborated at all, but I won't go into that, but there's a lot of very exciting things. Anyway, so it was all tremendously exciting, and I'd got a whole lot of new insights. So I went over to see Neil straight after that, and Neil was very excited too with what I was telling him about, what I'd learned about the three-body

1:22:30 problem and Christian Marshall, and he could immediately see a whole host of issues. Once you've got the idea of a relative configuration space and the technical term for it is a stratified manifold and I suddenly had a conjecture with the Frenchman I got a conjecture about the significance of the stratified manifold and these things. You can read about it in the end of time. I saw that that's got huge potential to change the way we think about dynamics and I explained that to Neil and he immediately saw it and if you ask Neil about it I mean Neil said to me when I last discussed it he said Julian if there's one thing I'm absolutely certain is is there to stay it's this inside of yours about stratified manifolds and the significance of their strata and things like that so I mean he's he's completely on board so to speak with that but I've hardly had a chance to write about it I mean that's going to go in this slim volume as well that's sort of going to be the conjectural part at the end but I can just give you some feeling of what it's like the this notion of a relative configuration space which is a stratified manifold the simplest one you can have is for the Newtonian three-body problem and and they all have a characteristic structure that's it's what's called a hierarchically nested I'll show you my model of configuration, relative configuration. They're all hierarchically nested and it's dramatically asymmetrical and the best matching idea that Brun and I developed always gives you a way of defining a geodesic principle on these stratified manifolds and then but what is the absolute joy about it is that you You can start with the simplest non-trivial one, which is for the three-body problem, which is three-dimensional. Or perhaps the even more fundamental one, which is what I call shape space, which is only where you consider the shapes of the triangles and not their sizes. And you can do the trick too. The really key step was that I found a geodesic principle on shape space on the two-dimensional one. That was the real breakthrough. But you can go on. And you can then go on to the four-body problem, the five-body problem, the N-body problem.

1:25:00 And they're all described by stratified manifolds. And you can do dynamics on them with best matching. You always recover either Newtonian theory or general relativity theory within this completely new framework. And each step you go up is giving you a hint how to go on because you've got a base on which you go. And it's a marvellous prospect of working our way up to ever more sophisticated theories. I think it is actually, potentially, without limit, actually, because you can always go on to ever more sophisticated structures and ever more sophisticated spaces. And you can draw on all the experience you've got from before. You can see that already with the work that Neil and I've done. And you can see the work with Bruno and then the conformal thing and the particle mechanics. And then you go into conformal super space and it goes on. And this will go on and on and on. It's really, it's a principle with unlimited scope, I think. So, no, I'm off to paradigm shift. I think it would be very interesting to follow. Let's go in in a moment and have a look. I'll show you my model and I'll give you a copy of my book. Great. I have one quick question before we stop and go in. I was interested in your way of working since you mentioned that you... Well, I got the impression from what you were saying that you don't necessarily spend a lot of time writing down equations. very little I think one hell of a lot I don't like doing equations I'm getting better at equations now I actually worked out the equations of the conformal particle mechanics actually the night after I'd spoken at Trinity College Dublin on the flight to New York and I actually got a result which I'm very proud of there's a new conserved quantity and it's the trace of the moment of inertia tensor and I got the calculation right so I'm very proud of that but I think it's partly because I haven't been teaching I suppose I was reasonably competent at doing calculations but I think it's partly because I haven't been forced to teach at university

1:27:30 so I've sort of got out of the practice of doing calculations and I'm a bit lazy to be quite honest Stephen Hawking said that he'd been forced to develop a good intuition because he wasn't able to do calculations anymore. And I think I'd say I was forced to develop a good intuition because I could never do them anyway. Right. And I think that is true. I mean, my way of working is, I get huge stimulus from reading good articles and books. I find, I don't think there's any, if you read really good articles by really good people, good books and things, I get a huge amount of stimulus and I don't need to be in any institute to do that. So the really decisive advances for me have been reading books which have then just set my mind thinking and I just cannot stop thinking. I mean, now for, I would say for 37 years uninterrupted, I have been thinking about space and time and motion and things like that. And it just never stops. It's going on in my head the whole time. in fact I actually put a footnote in the original draft in absolute relative motion I think actually I spent more time thinking about these things Carol said, Julian you've got to take that out Lee Smolin said I've got to leave it in but I followed Carol but I think now I mean, I just, and I love walking and I love thinking. I just go, I lie in bed and it just comes, it's like music. I have no control over it at all. It's just going on all the time. It's fun, I enjoy it. I like walking. Does it have a verbal or a visual quality or something on skin? Oh, definitely visual, definitely visual. Yeah, yeah, yeah. I'm definitely sort of moving objects and things around in my head and sort of... It's definitely visual, very strongly visual. No, I struggle, I ought to do more. I struggle to read sort of Barkey-type books and abstract algebra and things.

1:30:00 But I ought to do more, and I should read much more of Hamilton, because he had, I think, a very interesting way, his sort of process ideas, which led him actually to develop modern algebra, essentially. And that, I think, was geometrical and visual as well. get a, if ever I'm going to understand algebra it will have to be through visualization of what the action of rotation groups are and things like that and yeah that's the way I work and then I've had this great good luck of interacting with just enough people to help me, I mean I could never have done it without Bruno, I mean Bruno was the tremendously important one and then the encouragement from Lee. I mean, encouragement, even if it's only just one person, encouragement is so important. And then Jimmy York did it again, you know, it's just amazing. No, I think one must be very, very careful about criticizing people. You know, if it's wrong, you've got to say so, but you should always try hard, I think. If a young person comes to you and says, look, I think I've got a good idea, I would say, you know, it's really an obligation to try hard to see what that young person has got, and see if there's something there, and if it's good, say it's good. This was what Jimmy said to me too. He said, one of the real problems of young people is that they've often done really good work and don't I don't think that was ever the case with me I was always convinced it was important never mind about that but I think Jimmy is right and I mean it's my belief that we really owe the Principia to Halley I mean Halley claimed it he said I was the Ulysses who drew forth as Achilles and I think this one suave, polite young man who came to Cambridge and flattered Newton and said you could do this

1:32:30 Mr. Newton did the trick I think it, you know Newton, he'd already sold it Hook had badgered him into solving the problem and he'd done it but he still, I don't think, had got universal gravitation I mean, there's a wonderful paper by Curtis Wilson, which really completely persuades me that Newton didn't get universal gravitation in its full ramifications until very, very late. And it was the stimulus from Halley that made him sit down, and then suddenly it dawned on him what he got. And he got the theory of universal gravitation, and then it just unleashed the whole thing. And I'm sure it was just that visit from Halley, and a little bit of flattery and encouragement. You know, it's amazing. I guess maybe your experience suggests there's nothing like writing a book to stimulate... Oh, books are wonderful. I mean, the other thing which is really quite funny, I mean, I must say book, it's amazing how seriously people take you if you've published a book, never mind what the book is like. I mean, a year ago, it's a bit more than a handful of people knew me and I'd certainly already got quite a reputation worldwide in the history and physics community history and philosophy of physics community i mean they certainly you know i know that because i was asked to sort of give judgments on tenure applications and things like that you know and so forth but um shall we say in the theoretical physics community i'm sort of known to only very few people you know but now suddenly i'm an eminent theoretical you know you do laugh at it it's it's but that's that's the book that does it the book suddenly gives you that status that you just didn't have before even it's very interesting if a book is i think a book is my advice to anybody who really knows they've got something is not to rely on putting it out as a paper but to write a book you'll get a much bigger impact i think with a book if it's well written. That's certainly my experience. Shall we go up and have a look at my model?