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In the shadow of spacetime symmetry

In today’s blog we talk with Dr. Julian Barbour, PhD from the University of Cologne and maverick creator of Shape Dynamics, a cosmological framework within which the concepts of time and entropy are transformed. While the basic structure of his theory has been around for over 2 decades, many details have yet to be worked out, some of which we discuss. We also explore some of the sociological aspects behind the way his ideas have been received.

David: The current view of the universe involves forces acting in time to generate configurations of matter and energy. Time seems important. Since in your model, time disappears, what is the universe about? Is the universe in your framework the totality of configurations of different complexity and time is a label on these different states and in some sense it is then simply a statement about the degree of complexity?

Julian: Well, that’s a view that has become very sharp recently. I mean this has been a long journey. It all started really with me before I’d read Ernst Mach’s book coming to what he says there which for me is the beginning of all this story, which is that it’s utterly impossible to measure the changes of things by time. Quite the contrary, time is an abstraction at which we arrive from the changes of things. That’s been my guiding principle for close on 60 sixty years. It then crystallized around 1981. The key sentence that got me my collaboration with Bruno Bertotti, which was very, very fruitful, was one sentence in my first paper in Nature which was that the history of the universe is a continuous curve in its relative configuration space. And then I said if time doesn’t exist, that curve should really be a geodesic in the configuration space. It would just run through one configuration of the universe after another. And that really struck Bertotti, and the original idea for implementing Mach’s idea that all motion is relative, involved a Lagrangian, which actually, as Bertotti pointed out to me, leads to anisotropic inertia. It was first proposed without a distance dependence in 1904. Then Reissner, of the Reissner-Nordstrom solution, proposed two papers in 1914. Then Schrodinger wrote a beautiful paper in 1925 and he did estimates and he realized that the theory was on the point of being refuted if anyone knew a bit more accurately where the center of mass was of the galaxy and how much mass. And that same theory was rediscovered I think about 15 times in the 20th century. But the only person who actually took time out and made it a geodesic principle was myself.

And then it was later in 1980 where finally in discussion with Karel Kuchar it transpired that I just independently discovered Jacobi’s principle which for one given value of the energy you can describe the system as a geodesic in its configuration space. And then Bertotti and I developed this method of best matching, and as Bertotti soon realized, was just the gauge principle in the simplest possible form it can be. Our particle model with vanishing angular momentum I think should be regarded as the simplest non abelian gauge theory. That eliminated the problem of mass anisotropy and Bertotti and I did talk about trying to make the theory scale invariant. Our theory was invariant with respect to the Euclidean group but not the similarity group. Bertotti and I thought we ought to go on and make it scale invariant as well but we never got round to doing it. I was prompted to it twice by Donald Lynden-Bell. One at the Tubingen conference in 1993. He had identified himself as the referee of our 1982 paper in the Proceedings of the Royal Society. So that was one prod in ‘93 and there was another a few years later where he invited me to his college in Cambridge and we talked about it again, but very important bit by bit was my interaction with Jimmy York whom I’d visited in North Carolina Chapel Hill in the fall of ‘92 and was beginning to learn about his conformal treatment of the initial value problem in general relativity. Jimmy was wonderfully supportive and I said to him at one stage in our discussions ‘but surely you knew all these things about best matching’ in Princeton in the ‘70’s. And he said “No Julian, absolutely not. I was there. What you’ve told me is something completely new. And I’ll tell you what. The person you should try and work with is my first student Niall O’ Murchadha. It was Niall who proved the existence and uniqueness of solutions of the Lichnerowicz-York equation. Are you familiar with it?

David: No. I am not.

Julian: It is the solution of the initial value problem. Surprisingly few people know about it. I think it is the most important equation in dynamics. How familiar are you with the ADM formalism in general relativity?

David: A little.

Julian: There are constraints. Unless you have solutions to those constraints you can’t do anything with the theory. It’s just like the Gauss constraint in electrodynamics but that’s a lot easier to handle. Lichnerowicz had found a partial solution in 1944 and Jimmy built on that by trial and error. I think it’s incredibly important. I’m convinced of that. Niall summarized it when I started working with him back in 1999. He was interacting a lot with numerical people at that time. In the early 2000’s, he said of numerical experts that they come into the office in the morning and then set up a program using essentially the method that he and York had developed to find initial data and then next day when they’ve got the initial data they can start evolving the hyperbolic part of the Einstein equations. Still to this day there’s no alternative. The initial value problem is solved in a conformally invariant manner. And I would say that, as a dynamical theory, the 3-dimensional conformal invariance of the initial-value problem in general relativity is vastly more important than 4 dimensional spacetime covariance. I remember York saying to me if you can’t actually solve the equations of that theory and do something with them, you haven’t mastered the theory, you don’t know what you’ve got. And I think this is very true of a lot of people. If you read Bob Wald’s book on general relativity, which is very good, you’ll nevertheless find that the solution to the initial value problem is in appendix E at the end of the book. The book is about spacetime, not how spacetime comes into existence.

David: Why is this missed so much in the community?

Julian: I would say it’s the magic of Minkowski’s lecture in 1908. Have you come across Karel Kuchar?

David: No.

Julian: He was one of the great experts on canonical quantum gravity. He’s the person who called its fundamental equation the Wheeler-DeWitt equation.

David: Ah, yes.

Julian: Karel’s a great friend of mine. I visited him several times in Salt Lake City and on one occasion for over three months. It was marvelous. That was the winter of ’92-’93. Karel was a bit grumpy when we were talking about general relativity and discussing canonical quantum gravity which just is 3+1 and doesn’t sit comfortably with spacetime symmetry. And I said: ‘Karel what do you really believe in?’ And he started with the opening words of Minkowski’s famous paper "Henceforth space and time by itself are doomed to fade in the mere shadows and only a kind of union of the two will remain.” I think Karel was crucified by that dilemma between 4 dimensional covariance and the 3 dimensional requirement that you need in quantum mechanics. And in fact there’s a remarkable paper by Dirac in 1959 where he all but in 6 pages creates Shape Dynamics except that he does it in asymptotically flat space, not in a closed space. And 6 or 7 times, once in italics if not twice, he expresses the opinion in his earlier paper of 1958 that 4-dimensional symmetry is not a fundamental feature of the physical world. It was that remark which I picked up by chance in 1963 that set me thinking about time and asking, well, what is time?

John Wheeler coined the expression ‘superspace’ for the space of all possible 3-dimensional closed Riemannian geometries, and if you take out the scale of each space point you get down to conformal geometries, so there’s conformal superspace. And I would say vacuum general relativity is expressed as a geodesic in conformal superspace.

David: So in a sense Einstein was right again when he first criticized Minkowski on the combination of space and time in that way, putting them on the same footing.

Julian: I think so. Yes. I think there’s an incredibly beautiful parallel between the similarity group, which is a finite dimensional Lie group, and the group that I call the geometrical group. So when Riemann created Riemannian geometry he kept Euclidean geometry infinitesimally and just curved it. And that brought into existence, immediately, a group of 3 dimensional diffeomorphisms and 3 dimensional conformal transformations. I think it’s the semi-direct product, technically. And you could do what Bertotti and I did with the particle model and got solutions with vanishing angular momentum. You could do the same thing but in a much, much more sophisticated way with 3-dimensional conformal geometry. Clifford had suggested that 3 dimensional geometry, as Riemann had created it, could vary, it could be dynamical. And if Clifford and Mach and Poincare had got together in the late 19th century and tried to make a dynamical theory which was Machian, they would have discovered vacuum general relativity. That’s in the paper “Relativity without relativity” that Niall, myself, and Brendan Foster produced in 2002. What’s then amazing is that if you couple a scalar field to it, you get one condition: that it must respect the same light cone as the gravitational field. Then you try and couple a 1-form and you get 4 conditions. Three of them also say it must have the same light cone and a fourth one says it’s the Gauss constraint and it must be electrodynamics. So the whole of general relativity comes out in a totally different way. So I think it’s just a pure historical accident that the first problem Einstein solved led to special relativity, his 1905 paper. Which he did brilliantly, of course.

David: It put things on a certain course.

Julian: It put things on a certain course. And then equally brilliantly he was able to generalize from the Lorentz group to uniform accelerations. And then he thought it would just go on to all transformations. But he got in an almighty muddle. From when he tries to go beyond uniform accelerations it’s a muddle. If you look in the Tuebingen proceedings, you will find just one quotation I put in from him in 1918 where he said: “You would think that to create a theory in which motion is relative”- that’s not his exact words - “you would just say that the only quantities that should occur in the theory are the separations between the particles. This was attempted” he said. He knew Reissner’s paper along those lines. And he knew Schrodinger’s paper, which is essentially Reissner’s. And then comes Einstein's comment “but the history of physics shows that this was not viable”. What he means is that’s not the way he went. Einstein was absolutely brilliant. I always say he deserved about 6 or 7 Nobel prizes. But he left one almighty mess on Mach’s principle. And frankly Hermann Weyl was even worse.

David: Mach wasn’t very excited about general relativity.

Julian: It’s a bit unclear how much he understood. There’s a bit of controversy. I doubt if Mach really understood relativity. He seems to have had doubts about the light postulate and so forth. So that’s the picture that I had got to with Bruno Bertotti when I had the Janus-point idea about the arrow of time, which again was thanks to Kuchar. Karel challenged me because he claimed you could rewrite Newtonian theory in a way in which it is already Machian. How familiar are you with the wonderful book by Cornelius Lanczos, The Variational Principles of Mechanics?

David: Yes. I’ve seen it.

Julian: It’s a great book. You can go to what is called the Routhian; you eliminate a certain degree of freedom and you get a constant in place of it. Jacobi’s principle is an example where the energy appears as a constant in a geodesic principle. And Kuchar thought that you could do this for more degrees of freedom and this would give you a relational theory. So that made me really start looking at things. And then around 1982-83 I learnt about Lagrange’s result in 1772, which is that if the energy is not negative then the size of the system goes through a unique point of minimum. I’d always been interested in the arrow of time, but I didn’t put the two together until 2012, when Flavio Mercati and I were trying to get some research funding. Martin Rees had become a good friend because he really liked my book The Discovery of Dynamics. So I sent him an email saying did he have any suggestions. He suggested we should apply to funds that Templeton was doing but the University of Chicago was administering. So we wrote up a proposal on complexity or structure in the universe because I’d been immensely impressed when I read Leibnitz’s Monadology. It must have been late 70’s when I’d come across his claim that we live, not in the best of all possible worlds but in the universe which is more varied than any other one but subject to the simplest rules. So I was very interested in that. And somehow while writing that proposal I must have put together Lagrange’s result with the arrow of time. But the extraordinary thing is, it’s not in the proposal that we sent off. It’s not in any email I exchanged with Mercati. But there’s no question I did it then because there was a marvelous conference in Prague that Jiri Bicak organized in May 2014 because that was the 100th anniversary of Einstein leaving Prague and going to Zurich to get help from the mathematician Grossman to create general relativity. And I went to Paris by Eurostar, I suppose. And then flew from Paris to Prague and back and I arranged to meet an n-body specialist in Paris on the way back in the Gare du Nord station in Paris just to make sure that I was right. So I can date it. By May I must have had the idea because I had arranged this meeting. Anyway, everything just grew and grew from that. Fairly soon after that when I was visiting my youngest daughter in South Africa, I read Paul Davies’ book The Physics of Time Asymmetry, and at the end of it I suddenly felt to myself that if there is an entropy-like quantity of the universe it doesn’t increase but decreases.

David: Can I ask you about the relationship between entropy and information in your model compared to the standard explanation?

Julian: Well, there’s no doubt in my mind that the capacity of the universe for storing information is vastly greater now than it was just after the Big Bang. You might like to read a wonderful paper in the archive by Ted Jacobson about Carnot and entropy which I mention in my book. Ted has the idea, which he picked up from Lemaitre, that the Big Bang was really in the form of a crystal that decayed. And if you think about a regular crystal it can store incredibly little information. In fact, what’s now very important for me is if you have a Newtonian total collision: all the particles collide at the same instant at their common centre of mass. If run it the other way, it becomes a Newtonian total explosion, a big bang. Remarkably it starts from the absolute minimum of the quantity we call complexity. And the only information it contains is the mass ratios of the particles because they completely determine the shape at a total collision. So if there are N particles, it’s N-1 pure numbers that are encoded in that state.

David: So information is what in your model? It’s some kind of measure of the possible configurations or the actual configurations?

Julian: Well, I would say it’s still an open question. I’m struggling towards that. But certainly if you take the N-body problem with a lot of particles and it starts with a total explosion then the initial shape is unique. It just contains information about N-1 mass ratios. Later on when it’s evolved and there are sufficiently many particles, you can print War and Peace. So I think that’s what’s been happening in the universe. Now how you exactly quantify information is another matter. Of course the Shannon entropy is extremely interesting. I am a joint author of a paper on that which is on the arXiv with Gabriele Carcassi and Christine Aidala. It is going to be published in the European Journal of Physics. I think you can characterize distributions of things and their semantic content by the Shannon entropy. And I suspect that information about the semantic content peaks somewhere when the Shannon entropy is between its minimum and maximum value.

David: So there’s no strange or special condition at the Big Bang?

Julian: Well, if our conjecture is right it’s extraordinarily special. It certainly is in a Newtonian Big Bang. There’s no shadow of a doubt it's extraordinarily special. Our conjecture is that it is also in the case in general relativity. And the reason why people think it’s a horrible mess is because they’ve left in scale. The Hawking-Penrose theorems are about what happens to the scale factor. They made no attempt to see what the shape of the universe does. Well, to some extent what the shape is like is known from the so-called Bianchi IX model. Because of the singularity theorems, John Wheeler said general relativity predicts its own demise. Ever since then people have thought general relativity breaks down, space and time become discrete, and goodness only knows what’s going on. My collaborators and I have become persuaded of the opposite: that general relativity is at its simplest at the Big Bang. And that it could well be very much like what happens in a Newtonian total collision. The justification for thinking that way is that in both cases the scale goes to zero. And something going to zero is an incredibly strong restriction on what can happen.

David: So in the current picture, the Big Bang is special and mysterious. In your picture, the Big Bang is special but not mysterious.

Julian: If we have understood it right, it’s not mysterious. It would be a very definite picture of what the Big Bang is like. There’s a lot of work to be done because at the moment we don’t know what will be the effect of including matter. We know a bit about vacuum general relativity. Our complexity is bounded below but unbounded above, which is exactly what you want for time which goes from zero to infinity. Time never ends.

David: Is it fair to say that you have argued the second law of thermodynamics doesn’t apply in the way that people think? This is true even outside your own model.

Julian: I would say thermodynamics is definitely secure for you and me. We’re going to die. And steam engines will never achieve more efficiency than Clausius and Thompson established in the 1850’s. But I’m more and more persuaded that it’s very misleading if applied to the universe at large. It’s very interesting if you look in cosmology books. I think they use a valid notion of entropy when the universe really is Friedmann-Robertson-Walker and it’s in thermal equilibrium. Then basically the cosmologists notion of entropy is usually a simple count of the number of quanta that are there. And the universe cools a bit as it expands, you get various neutrinos freeze out and things like that. And there are changes in the total number of quantum states in a spatially closed universe. And if you count them that’s fine. But the problem is the minute the universe becomes inhomogeneous it becomes very questionable. I think Kelvin set people off on quite the wrong road when he spoke of dissipation of mechanical energy because dissipation is such a negative word. But if you look at the water drops as they fall into a stream and create concentric ripples the effect is beautiful. The energy has been spread out. The term dissipation is very misleading. I would say there is a whole spectrum of different possibilities for energy to spread. And if you’re in a universe that is expanding, I don’t think you could say that it is creating disorder. Think about stirring up water in a bath and then letting it subside and it becomes flat. People say a whole lot of disorder has been created. I would say it has created a nice smooth surface. Thermodynamics and statistical mechanics is an absolutely brilliant lie. It was brilliant for all the things that it led to, the discovery of the size of atoms, quantum mechanics and all these things. But there is no properly confined system in the universe. They’re all, ultimately, in some sense open.

David: Is it the openness that makes this entropy idea incorrect?

Julian: It makes it very dubious. In the great bible of statistical mechanics by Willard Gibbs in 1902, he says in effect he is going to develop the theory in complete generality for any Hamiltonian system but that he must introduce two restrictions which are not really to do with the dynamics but with the fact that he is going to talk about probability. The system must not be allowed to expand into infinite space. And the momentum must not grow too high. Those conditions, certainly not the one on spatial restriction, are simply not met in the expanding universe.

David: It’s not surprising that this happened in the 1850’s, 1860’s in a context in which people knew nothing about expansion.

Julian: They knew nothing about expansion but I’ll tell you what. I haven’t checked all the literature carefully but I have looked at a lot of the papers and books on the problem of the arrow of time and entropic increase. I have not once come across anybody comment on the question of whether things are changed in an expanding universe and the fact that thermodynamics and statistical mechanics presuppose perfect insulation.

David: And why do you think that is? Is there no realization of a fundamental difference there?

Julian: I think it’s just people don’t shake off what they’re taught. I cite Mach that the study of history of science is very important because ideas that are brilliantly successful can outlive their time and then hold things back.

David: You go to conferences. You see academics who think in terms of entropy increasing. They’re convinced by it. What do they reply to your ideas?

Julian: Some of them, among them Carlo Rovelli, just think I’m mad. If you read Roger Penrose, it’s an article of faith for him that there’s an entropy of the universe and that it increases. If you look carefully there’s a critical place in the Emperor’s New Mind where it’s quite clear he thinks the universe has a phase space whose Liouville measure is bounded because he bases his calculation off the incredible figure, 10 to the 121, he calculates for the entropy that the universe should have had at the Big Bang. His calculation implicitly uses the recurrence theorem. But the recurrence theorem does not hold if the phase space does not have a bounded measure. And people are just unaware of that. Sean Carroll’s book From Eternity to Here – which is really quite nice – has a whole chapter on the recurrence theorem. At the start he does point out that it only holds if the system is bounded in space. But later on he quotes with approval Feynman, who completely got it wrong, who argues with systems in a box.

David: But someone must explain how the ideas behind closed systems apply to expanding ones.

Julian: I have not found them. I think there are various explanations for their absence. One is the tremendously strong foundation of phenomenological thermodynamics based on the impossibility of building either kind of perpetual motion machine. That was very powerful. Then Clausius was a very successful salesman of his idea of entropy, saying that there were two fundamental laws of the universe: Its energy is constant and its entropy tends to maximum. And then there is the famous saying of Eddington: "If your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation". I just think people haven’t thought about it. They just take it as an article of faith. It’s the same with the foundations of dynamics. When students are learning dynamics at the age of 16 at school, they ask how can you say a thing is moving in a straight line in an empty space and the teachers say ‘don’t ask questions like that’. I’ve come across several people who had that experience. As long as the foundations are secure enough for what you’re doing, that’s fine.

David: As long as there’s enough practical work to do, you don’t question the foundations.

Julian: Exactly. A lot of people don’t question the foundations. It’s very true. And it’s very difficult to do that if you’re in academia. That’s why I became an independent, because I could see the danger. Even in the late 1960’s "Publish or perish" was already a common expression.

David: If you force people to publish too much, they’re going to say nonsense?

Julian: It might not be nonsense. But very likely it will be churning or tweaking. Just look at the arXiv every morning. Thank goodness for gravitational waves. At least many things I see on the gr-qc arXiv is pretty solid stuff.

David: I’ve seen some of your videos. I’ve read some of your papers. You express your ideas with a mild tone. You’re not very confrontational. Do blatant misconceptions of your work not affect you deeply?

Julian: Uhm… I think I’ve become fairly philosophical about it. It was very difficult to realize to what extent my papers were being read. Eventually, I discovered that quite a lot more people were reading them than I knew anything about. You’re an example. But they’re not working in the field. Therefore, they don’t cite it and they don’t get around to saying ‘Oh look, I’ve read that and I find it very interesting’…. I don’t know. I’ve been so lucky in life and so enjoyed being alive. It’s not the end of the world if I don’t get recognized. I can say that’s honestly true. I used to play golf for many years, not to any great standard. I miss the golf course but not the golf. But I remember one day we’d been talking about drug taking with the chaps I was playing with and it occurred to me that it never entered my head to try drugs because I didn’t feel the remotest need for any excitement beyond what I was already getting. And another thing is that after my PhD I was financially independent, earning my living by translating Russian scientific journals while still having time to research, so I didn’t need to build up my publications and citations which took a lot of concern out of the thing. Initially, I was recognized among physicists because of my book on the history of dynamics. Martin Rees read it and was very enthusiastic. He suggested I should appear on BBC programs and things like that. Bill Unruh was hugely enthusiastic. Have you seen Bill’s endorsement for The Janus Point?

David: No. I haven’t. But I did see your interview on Closer to Truth (

Julian: It's very encouraging. And in an email to me Michael Berry said about this business about the universe not being in a box: “I love it!”.

David: Thank you so much. It’s been over an hour.

Julian: It’s been great talking to you David. Let me just say that one thing that could undermine Shape Dynamics is black holes. I keep on hoping someone will find out what black holes in a spatially closed universe are like. All the work of people like Penrose assumes asymptotical flatness. I asked people like John Barrow and George Ellis what’s known about black holes mathematically in a spatially closed universe, the answer is invariably: ‘not much’. Frank Tipler apparently made a few interesting remarks 40 or 30 years ago. I asked a famous mathematician why they always study black holes in asymptotically flat space and not black holes in closed spaces. He said that without the condition at infinity, you can’t do any mathematics. For me that’s a very critical issue for Shape Dynamics.

David: It’s hard to even interpret these things physically in a closed universe.

Julian: But somehow my intuition says that shouldn’t be impossible. I may be too optimistic because the Newtonian theory is so transparent. I think the notion of a conformal geometry with matter fields is tractable. One last comment, David. I think you have to peel away everything that is redundant. The reason why I have faith in Shape Dynamics is that you’re using dimensionless pure numbers. You are not losing one iota of physical information and you are scraping away everything that is redundant. Then you see the universe for what it is. That has tremendous transformative possibilities. And that’s what’s led to this latest idea of the real nature of time at the end of my book. And we’re working on a paper about that now.

David: You don’t talk much about space in your papers. The focus is on time. But space for you is relational.

Julian: Yes.

David: The notion of something being close or far away in space must be related to degrees of differences in the configuration space. Does this parallel with recent ideas that connect spatial distance to quantum entanglement?

Julian: I have not got into entanglement with anything like the depth that’s needed. What I do think is that angles at spatially separated points do exist, at least at the classical level. I’m beginning to think that space may remain continuum based. And quantum mechanics gives different probabilities for different conformal geometries. The best account of this is in Mercati’s book “Shape Dynamics”. I think it may turn out to be that the whole idea that space becomes discrete and granular in the quantum-gravity regime might be quite wrong. There’s a chance at least. That would make life a lot easier. I mean loop quantum gravity has been struggling to recover the continuum. I don’t think they ever will.

David: You’re on a collision course with Carlo Rovelli.

Julian: Yes, I know him well. He uses the word relation a lot. That actually comes from me because I passed it on to Lee Smolin and Lee on to Carlo. But Carlo's responsible for what he did with it.

David: I’ll transcribe our talk and send it to you.

Julian: Good to talk to you.

David: Thank you Dr. Barbour!

Julian: Pleasure. By for now.

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