Against Symmetry — Platonist vs Relationalist Responses to Crisis in Theoretical Physics

0:00 Thank you. Thank you. Thank you. I have noticed that does tend to be a Parisian custom, and if it's any consolation, the more distinguish the speaker, the later they tend to start. Well, then we should have started then. OK, I'm going to switch to English right away. The whole talk

2:30 and discussion will be in English. This is the first of Parisian parts, in Canada, who's done work mainly in cosmology and quantum gravity, but who is also very interested in issues relating to philosophy of physics, philosophy of space-time theories and of quantum theory, so various, various kinds of problems and questions. So, you may know of his professional work, but he's also authored several popular books about gravity and cosmology. He's been taught in Paris this week on different subjects, more at Spelicions, and Dr. Timore at Beaux-de-France. And this is the first talk on, if I may, more philosophical matters, it's a non-technical will be some physics, of course, too, and the challenge behind this talk is that here at CREA, at this event, thanks to its director, there has been a lot of debate that you may have heard about various kinds of neotranscendental approaches and other interpretations, all All of them preys in symmetry, and all of them taking symmetry as a basic constitutive feature of physical theory and of human knowledge in general. And this is a talk that we're hosting here that has this challenging title both for us and for all of you, against symmetry. So we're hoping to hear some radical, or maybe not so radical, but still a critique of the kind of work that has been done in this lab. It is my pleasure to introduce Lee Smolin. Thank you. Thank you very much. It's an honor to be here, and I apologize at the beginning for speaking English. It was great to have a speech, but if I speak too fast in English

5:00 too locally New York English, somebody will tell me and correct me. It is an honor to be here. I haven't given, I realize I haven't given a talk in Paris in about 20 years, although I've been many times other places in France, particularly Marseille. And all of a sudden, so it is an honor all of a sudden to be giving three talks, and they are related very closely in fact. In fact, they're also related to a talk, I noticed some people from London at the London School of Economics, which is a different aspect of the same theme, the meaning of relationalism. This talk, which I'm very grateful for the invitation for, is a more philosophical talk, although I'm not a philosopher, and I'm looking forward philosophers on the more correct ways to say and think about the things that I'll be trying to say here. The talk tomorrow is a popular talk, but very closely related, and a talk Friday at the Cosmology Institute slash College of France, which I think is at 2 o'clock, is a science talk, but I'll be mentioning towards the end of today's talk what the key ideas or key themes. That's a sort of just update on what's happening in our group's scientific work, but it's closely related in ways that I'll be able to say later. The title of Against Symmetry, I have to say, was given me by our host without knowing what he just said, which is that this is intended as an intervention in a conversation about symmetry, which I didn't know. I'm glad to see that there's a big supply of fire extinguishers there in the back, if anybody noticed, coming in. But this talk is not consciously controversial. Indeed, from my point of view, very old tradition as will become clear as we go along. So for me this is a visit to an

7:30 old tradition rather than something attempting to be provocative. So there are, it seems, two traditions in the present day search for fundamental physics. And before I go on, I want to say that the background for these thoughts and for giving time is what a growing number of us perceived to be a crisis in fundamental physics stemming back from the mid-1970s. And the best way to say it is that for the roughly at least 200 years before the mid-1970s was a period when fundamental physics grew rapidly and And constantly, so that roughly speaking, every decade, there was a major new development in which theory and experiment went hand in hand. And the last triumph of which was the standard model of particle physics invented in 1973, which is still the best model we have of elementary particle theory. And with the possible exception of the theory of inflation in cosmology, which was 79, 80, 81, depending on who you think you should attribute it to, there has not been a new theoretical development that was confirmed by a new experiment or a new experimental discovery that was explained by theory. And for a growing number of us, this is a crisis, and this talk is part of an attempt to find the roots of the crisis, which I believe there is a crisis, and I believe there are roots in an intellectual mistake, and the intellectual mistake is about which of these two traditions is the appropriate tradition to be carrying theoretical physics forward. I'm not going to try to make an a priori argument for one tradition over another. My point of view as a physicist is pragmatic. There are different philosophical traditions that are helpful at different times to further our project of understanding nature. And my overall claim will be that one project which was very useful into the 1970s

10:00 has worn out its welcome and we need to return to another. So, the project that I think, or the philosophical tradition that I think has outlived, at least for the time being, its usefulness, is the book's satanic tradition. And here, I apologize to people who are real philosophers and who might, for example, really have read Plato and understood him. so this is a physicist's understanding and the idea is of this as we understand as we call each other physicists when I call Roger Penrose a platonist which I will and he'll smile this is what I'm talking about the idea that there's another realm of reality besides the realm that we investigate experimentally in which laws are revealed in their most preferred form and there's a close relationship between perfection and the notion of symmetry, and on the one hand between lack of symmetry and decay or distance from perfection. And this, to my understanding, goes way back in the philosophical and indeed the Western literary tradition altogether. And just to be sure, what I mean as a physicist by symmetry, just to give one definition, is an operation by which two physically distinct entities are exchanged, one for the other, or one physical entity is transformed with respect to others, say this pen is moved from here to here, in a way that doesn't change the physical properties of either thing under an exchange or of the pen under a motion. More technically, the energy of the system, the Hamiltonian, which is the function that describes the energy as a function of the coordinates momenta is unchanged under such a transformation and the emphasis here is that a symmetry is a transformation between physically distinct configurations and this is very different and to avoid confusion at the very beginning we have to say this is very different from what's often called the gauge symmetry but symmetry there is a misnomer a gauge transformation which is a transformation between different mathematical descriptions of the same identical physical situation. And I want to make it very clear that I'm drawing a distinction between them.

12:30 When I use the word symmetry, I mean a transformation amongst physically distinct configurations or histories. So, in the modern version of the Platonic tradition, which we high-energy theorists practically grow up with as we're taught quantum mechanics and quantum field theory and so forth in school, there's an instantiation of this in which there's this idea that the laws of nature, i.e. the Lagrangian, of elementary particle physics is most perfectly probed in the limit of high energies, which is short distances. And that the imperfect realm of our experience, the fact that the experiments don't see a world which has a large symmetry group in it, a large group of such transformations, is a consequence of the phenomenon of spontaneous you know, as elucidated by Brought and Engler and Higgs and so forth in the early 60s, a quantum field theory can have a ground state where not all the symmetry of the dynamical laws are expressed. And there comes with that the idea that of a close related idea, which is unification, that the goal of theoretical physics is to unify all the different disparate phenomenon into a simpler description, a more fundamental description, and this more fundamental description will have more symmetry. And there's a thing that you're taught as a high-energy theorist, which is the more fundamental the theory is, the more unified it will be, and the more symmetry it will have. And that is the larger, technically, the group of symmetries will be, group of symmetries of the theory. Elementary particles in quantum field theory are classified by the symmetry groups that they transform under, both the symmetries of space-time, the Poincaré group is the one most often spoken about, and what's called the group of internal symmetries, the symmetries that interchange particles at the same place or the same history in space-time.

15:00 that the ground state of the system should have as much symmetry as possible. For example, there's the assumption in quantum field theory that if you're doing quantum field theory in Minkowski spacetime, the ground state should have the full symmetries of the spacetime. Now, there may be the phenomenon of spontaneous symmetry breaking for internal symmetries, but we always work under the assumption that the ground state of a quantum field has all the symmetries of the background space-time in which they're confined, and related to that is that this whole discussion of symmetries and this whole point of view relies on the framework of a background space-time. That is, this way of thinking about physics starts with the assumption that there's a space-time geometry which is given to us, which has maximal symmetries itself, either Minkowski space-time or Jussida space-time or anti-Jussida space-time, and that we are describing physics moving, quote, in the background space-time. And whether we're doing quantum field theory or string theory or whatever M-theory is, we're always talking about physics in a background, things moving in a background space-time. So that's one tradition, and it's certainly a tradition of what one might call an elementary particle physics. It's the dominant philosophical tradition which guides the thinking of elementary particle physicists. There's another tradition, and the other tradition is some of us think, again, I'm not a scholar or a philosopher, but some of us think of this as a Leibnizian tradition. And for us, the fake history that, you know, there's a difference between real history and of equal interest for this kind of discussion, the history that scientists tell each other and mythologize about to explain to each other why they disagree. So, in the mythological history, there was a debate between Newton and Leibniz in the period when Newton established a way of doing physics closely related to the view I just discussed. And Leibniz was one of the dissenters, not the only one. There were others, for example, Kuygens, but Leibniz is somehow the figurehead of the dissent

17:30 from a Newtonian point of view. Leibniz's discussion can be started off with the principle of the identity of the indiscernible, which says that if there are any two entities in nature with the same properties, they must be identified. So, by definition, this means that if you express the laws of nature in terms of the fundamental identities, and fundamental entities, whatever they are, whether they're particles, prints, strings, fields, whatever, and you believe in Leibniz's way of thinking, in particular you accept this principle, then there can be no symmetry, fundamentally, because Every time you would say that there are two configurations which have the same energy, or there are two particles which could be exchanged without changing the energy or the properties of each, by this principle of the identity of the indiscernibles, you would be forced to identify them and say there are two distinct things. So the Leibnizian point of view attached from the very beginning the use of symmetry the way symmetry is developed in particle physics and indeed this goes all the way back after all, one of the intents of Leibniz was to attack the Newtonian conception of absolute space and as in the famous correspondence it's attacked it using this principle and the principle of sufficient reason by saying that if there was a symmetry in space, that is, if it were possible to move the universe ten feet to the left without changing any of the relative motions or distances, then nothing would change in the future history of the universe as far as could be observed motions, and therefore that symmetry of being able to translate freely in space cannot be allowed by the correct formulation of the fundamental laws, because it disagrees with this principle and the reasoning that led to this principle.

20:00 And Leibniz is perfectly clear about that, and the same argument applies to the way that space-time symmetries used now on field theory and string theory, etc., as well. And so this is a contrary tradition. Now, this implies that there are no absolute properties defined with respect to an eternally unchanging background. That is, the notion of what is a property in Newtonian physics and the physics that followed up to and including quantum field theory is that the properties of a particle or a field are defined with respect to the geometry of space, which is presumed fixed. And so the properties that physics deals with, position, velocity, momentum, energy, are all defined with respect to a space which is an unchanging geometry which is given once and for all and whose use is to give properties to the entities that then evolve dynamically, namely the particles or, in the modern version, the fields. Leibniz's reasoning attacks that way of doing physics and asserts that there can be no properties defined with respect to an absolute fixed background because then there would be symmetries and then there would be a contradiction. And he then makes a proposal for how to do physics without properties of dynamical things defined with respect to an unchanging space-time background, which is in terms of relational properties. That is, he proposes that the properties of any entity in the universe should be about relationships between that entity and other entities in the universe. So-called relational properties. Then he starts talking about monads and all sorts of stuff that I don't understand at all, and maybe somebody can explain to me. By putting Leibniz here as the figurehead of this tradition, I don't want to buy into, there's a lot of Leibniz that mystifies me.

22:30 But in the writings that express the ideas that I've discussed, the aim is right on to the vulnerable points in contemporary physics. I suppose that the monads and all that stuff was a way in Leibniz's mind to construct a relational theory of nature, and I don't understand enough of it to know whether he succeeded. But he certainly did not succeed in formulating a mathematical framework that could be a genuine competitor to Newton. That had to wait quite a bit. Now, it's interesting, just as a side effect, this tradition was passed to those of us who work now in quantum gravity two people in particular John Stanchel and Julian Barber especially Julian Barber who did parenthetically what Leibniz ought to have done which is invented a form of particle dynamics purely in terms of relational quantities and had Leibniz done he perfectly well have, and has Leibniz formulated dynamics as Barber and his collaborators did in the 1970s, then who knows how the history of these things might have gone. But in any case, Leibniz did not do that, and surely the Newtonian approach to physics triumphed for some time. Okay, so here's just how they line up against each other from what I've said so far. So what I'm calling the Platonic and what I'm calling the Leibnizian tradition, their use and the meaning of space is completely different. It forms an absolute background against with the properties that dynamical entities are defined in a platonic approach. Now, a Leibnizian approach, there is, at root, nothing special that you would call space. There's a network of relationships amongst the dynamical entities, and the notion of things, quote, in space must somehow emerge from that network of relations. Properties, again, are, as I just really just said it, are defined with respect to this absolute background, or are defined relationally. Dynamics, then, must be formulated as just hinted in a very different way. We all know how to formulate dynamics in a background.

25:00 How to formulate dynamics without a background is a subtle problem. And I'll come back to that. It took longer, in spite of what I said about maybe Leibniz would have figured out what Julian Barber and collaborators figured out, actually, maybe not. I mean, there are that I'll be discussing in a minute about how you formulate dynamics without having a fixed absolute space of configurations, well, not configurations, of positions in which things move. This tradition leads to the notion that you want as much symmetry as possible in your theory. This tradition says there should be no symmetries in the theory. At the level of non-quantum physics, the highest instantiation of this is Newtonian dynamics and all its versions, both particle and field theory. And the highest instantiation of this, as I'll develop in a little while, is general relativity. And the interesting thing for the present day is that there are different approaches to resolving the present-day crisis of physics, which means making a theory which brings together the successes of quantum theory and quantum field theory with the successes of general relativity. And there are all the different approaches, of which there are many, which have larger and smaller groups of adherents and workers on them. And a few of us, hard to note, of disagreeable people who insist on not being classified and jumping among them. But the approaches really can be cleanly classified by this distinction. String theory, as formulated so far, after 35 years of development, there doesn't seem to be any change in this, is clearly in this platonic description. It describes objects moving in background geometries that are static in time. That's what actually, there are words that have more ambition to them, but in terms of what the mathematics actually does, that's what exists. And basically all the other approaches to quantum gravity, causal set theory, dynamical triangulations, non-community geometry,

27:30 quantum gravity, fall into this Leibnizian tradition. about non-commutative geometry, would you not agree that Fusy's space is a space with a different geometry, but it's some kind of background? I hesitated, that's why it's last there, because I hesitated about where to put it. And I think there are different points of view towards what non-commutative geometry is. and there is a point of view in which a non-commutative geometry is some particular space-time geometry just not one in which coordinates commute or algebra is a function or a commutative but there is another point of view about non-commutative geometry which is perhaps deeper which my understanding is false here but we could discuss that later maybe I'm anticipating here Okay. So what's interesting here is that the debates which are large and are heating up and are not always done with the spirit of generosity and rationality as befits intellectuals between these different approaches really mirror the debates going back in the history of physics and philosophy all the way back to the period of Newton and before. And it's very eye-opening when you realize that what you want to say to your colleague in the office next door is really just a mirror of what Leibniz was writing to Clark so many hundreds of years ago. But it really is true, and part of the purpose of this talk view of that. And so it's an ancient, I don't know about ancient, but it's a hundred years old debate, and it makes it, I think, both friendly and more rational to understand what we're really arguing about. And I think what we're really arguing about is the appropriateness of these traditions. Okay, now, let me talk first about the Platonic tradition and its

30:00 present crisis, because it has been the dominant tradition at all in the department of physics. It's the tradition that I personally was trained in as a quantum field theorist, sort of a representative of the first generation of quantum field theorists trained after the it's in crisis, and why it's in crisis has a lot to do with the tradition that it comes from. So, the search for a completion of theoretical physics from the standard model of particle physics has been the goal since the middle 1970s, and indeed the standard model of particle physics, its establishment was the gold for the previous decades. There are two big ideas which tie all the search and elementary particle theory into the photonic tradition. First, the idea of unification, that if we see different interactions, the strong interaction, the weak interaction, the electromagnetic interaction, the super-weak interaction, maybe the cc-breaking as it used to be talked about, that these are all there's a hypothesis that these are all manifestations of a single interaction this is a hypothesis that could be true or could be false but it's a governing hypothesis for most people who work in this field and there's a related idea which is symmetry that this unification of the different forces is to be achieved symmetry in the laws of physics. And there are two ways that this has been done. First, by increasing the transformations amongst the different kinds of particles, so for example, to extending to increase the SU symmetry which relates the quarks to a symmetry that includes also the leptons, the non-strongly interacting particles, perhaps SO5 or SO10. And let me remark again, I'm always talking here about global symmetries, although many of these things are also gauge symmetries, but I'm postponing the discussion of gauge symmetries.

32:30 I'm talking about symmetries in the sense of conserved charges that commute with the Hamiltonian that really generate physical transformations. the other way that this has been tried and there's a long tradition of this is by increasing the dimension of space so that some of the symmetries of space become symmetries of the elementary particles and just for fun, does anybody know that the first paper in this tradition I'll say within the 20th century I don't know if this is known What was the first proposal within the 20th century for unification of the interactions by increasing the dimensions of space? It was not Collucia. No, it's not Collucia. It's Norwegian, yes? What? It's a Norwegian one. Yeah, it's Nordstrom in 1914, before general relativity, to incorporate general relativity increasing the dimension of Minkowski's space by one. So, and I didn't even know that when I first wrote this, the first version of this slide, but this really starts with Nordstrom. And then, of course, there was general relativity. Luckily, there was experiment, so there were these two notions of unification. Nordstrom's higher-dimensional unification and general relativity around at the same time. Clearly, the more rational conservative alternative was Nordstrom's, but luckily there was experiment that settled everybody in the direction of general relativity, which is not the way the story is usually told, but as far as I can tell, that's the real story. The real story is that general relativity was some triumph of rationality that had nothing to do with the experiment, but indeed there was a more rational alternative. Nevertheless, as soon as general relativity was formulated, even before the first papers in 1915, Einstein, Hilbert, and others were already trying to unify gravity with Maxwell theory and perhaps other forces by various means, including extending the dimension of space and this is a whole tradition which ran until the middle 50s when

35:00 Einstein died and more or less died with him. And it's interesting, let me just say parenthetically, that Einstein was at first an enthusiast, he remained an enthusiast of unified field theories, but he was at first an enthusiast of the includes a Klein idea of unification through higher dimensions. But already by 1923, he had decided it failed. And he decided it failed, and I don't have the exact quote, but he understood and clearly formulated in correspondence the objection, which is that either you have to freeze the geometry of the extra dimensions. and those of you who know these theories know that this is true, either you have to intervene and choose only when you extend general relativity to five or six dimensions to unify with other forces, you either have to freeze the geometry of the extra dimensions to get what you want out, in which case it's not a unification because you're treating the other dimensions differently than you're treating the three dimensions of space, or you don't freeze them in which case the solutions you want are unstable and the instabilities quickly evolve either to singularities or to the extra dimensions blowing up and being like the dimensions we see in disagreeing with experiment and that's why these theories fail and Einstein understood that by 1923 therefore most of his work on unified field theories went in other directions The second try, of course, at this path to unification has been all the beautiful work in string theory. And even though in the end it's in crisis, it was beautiful work, but it led to, roughly speaking precisely the same failure, only compounded because more dimensions lead to many more choices of solutions and much more instability. And the process of fixing all that instability led to a crisis I'll come to in a minute. But it's the same idea, the same crisis. Okay, so where are we on this approach to unification? So the present evidence is that on some fixed backgrounds, string theories are consistent

37:30 to second order of a certain perturbation theory. and that's a triumph and that took in fact until 2001 to establish the consistency to second order and perturbation theory and the remaining question of consistency finiteness and so forth is open since 2001 however there is evidence nonetheless for an infinite number of string theories which in which The geometry of the extra-dimensions, there's an infinite number of string theories where the instabilities I just referred to have been stabilized. This is what's called moduli stabilization, and this has worked since 2003 theory from Kalash and Khatru and others, their collaborators and others. Even if you put on the constraint from observations that there's a positive cosmological constant, there's still at least 10 to the 500 distinct theories where these instabilities get stabilized. And I should choose my words carefully. There's evidence for the existence of these theories. There's no formulation of these theories in closed form or even in a perturbation theory, but there's evidence that they're existent. And we face a peculiar situation in which there's a small number of theories that are understood in enough detail to compute at least a second-order in perturbation theory, but they are in space-time backgrounds that are static without cosmological constant, and there's evidence for a vast number of theories that we can't compute with, agree with observation and that's the situation that we're in and that to many people is a crisis because and this was anticipated back in the 80s resembled by Andy Strominger in 1986 there's a crisis of predictability if there are so many versions and this comes from the possibility of choosing making many choices for the geometry and the values of fields in the higher dimensions if there's so many choices then there is a crisis of predictability

40:00 and that was anticipated by Strominger in 86 and it is indeed the crisis that we face leading to a lot of discussion and questioning at least on our side of the ocean I don't know what's going on in discussion over here Now, it's been conjectured that all these different theories are unified in one big background-independent theory that would be in the other tradition, that is a theory without the needing to define things moving in a fixed background, and that conjecture has a name, it's called M-theory, but despite much effort, this theory has never been formulated, which is another aspect of the crisis. It would certainly be wonderful if M-theory exists, but it's a name for a conjecture. It's the name of a conjecture about a theory. It's not, unfortunately, and this is something I've devoted some years to, and it's not easy. And even much better people have devoted even more time. Okay, so there is a crisis. what happened about this idea that the more unification the more symmetry and the more uniqueness so I didn't emphasize this before but there has also been a kind of guiding hope that as you unify more and more the constraints of having to satisfy all the symmetry principles of having to be in variant in space time unitary in Hilbert space trees would introduce more and more constraints which would narrow the options, leading to a unique unification. Unfortunately, it's gone the other way. The standard model from 1973 of elementary particle physics has about 23 parameters, depending on precisely how you formulate it, how you deal with neutrino masses and so forth. Its simplest supersymmetric extension, I didn't yet mention supersymmetry, but it's an extension of space-time symmetry, which mixes in internal symmetries of particles, which is essential for the projects of further unification and essential for the existence of string theories. The simplest supersymmetry extension of the standard model of elementary particle physics has 125 km parameters,

42:30 and the number of distinct string theories that have the possibility to reproduce those is 10 to the 500, although it should be said that so far there is not one of those 10 to the 500 in which there is a completely explicit realization of any of the previous ones, although recent work by Bert O'Byrd and collaborators is coming close as they hit the thing on the head with the exception of about 25 master scalar fields that shouldn't be there because they disagree with observation to give good force kind of effects. But they're getting closer. In any case, this is the number of theories that incorporate chirochromions, gauge fields, Higgs fields, and so forth of the kinds of stuff that goes into these unified theories. So it appears that the more symmetry and the more unification, the more three parameters and the less uniqueness and not the reverse. That's the experimental situation. So what's going on? I'm not going to answer that question right away. The question that has been most discussion about about, is what to do about it. And on my side of the ocean, I hope that there's more rationality on this side of the ocean, especially here, which is the home to rationality, historically, there tends to be more and more discussion about an idea called the anthropic principle. And the idea of the anthropic principle says, rather than hoping that the end of theoretical physics is the construction of a unique theory with maximal symmetries that then where the symmetries breaks and you get predictions for everything we see and everything we will see in the next years. Instead, there is a scenario where you have a vast number of theories, but a vast number of universes are created where those theories may act. And there's some little cosmological scenario which is very, not very rigorous and not, you shouldn't but if you just sort of believe the words, it can populate a vast number of universes with a vast number of theories. And then you apply the anthropic principle, which says if there are a vast number of universes with vastly different laws throughout them, then we should expect to see ourselves in a universe

45:00 where intelligent life can exist. And all the choices that elementary particle theory explain why we see the particular set of particles we see, why we see the particular set of symmetries we see, why the different parameters of the standard model of all the masses and strengths of forces have the values that they do, come down to, it's hypothesized, there are universes in which every possible choice is made for those, or at least that live in that world of 10 to the 500 string theories, which is quite a few, and there is no reason to believe there should be difficulty populating a wide range of choices for the things we see in those 10 to the 500 theories. So all that we should expect to be able to do this rationally is that we live in a world where we can exist, and that should be the foundation of our explanation of everything that's unexplained so far. And that is called the Anthropi Principle, and it has very, very smart and accomplished people have been its advocates, and in fact, recently you can add Steve Weinberg to this list of its advocates. So this is not to be disrespected, it's an idea that some of the most successful scientists in this whole area have embraced and are advocated. And I think that that's a crisis, and I think it's the reducto ad absurdum of this tradition, which means we should examine the contrary tradition. And I'm happy to come back and discuss in microscopic detail, if anybody wants, the arguments for and against this, because again, in our part of the world, an enormous amount of time and effort the last three or four years has been spent arguing about the adequacy of this kind of explanation. For example, Lenny Suskin, who is one of the people I most admire in my profession, recently published a book, I don't know if it's in French, but it's in English, in which he basically says that it's either this, or to go back to the notion that God created the universe

47:30 so there would be intelligent beings that love him. So, snakes are high. So, my main theme, is to go back to the other tradition, relationalism of the Leibnizian tradition, which I'm now going to define with a little more care. I will argue that we should believe in it, not just because there are good philosophical arguments by good philosophers like Leibniz Mach and people in this room, but because at least the theories that are much more timely constrained and hence are more and hence avoid the crisis. That's my theme. Now, I don't know how much time I have, so what I'm going to do is I'm going to define what I mean by relationalism in physical theory a bit more precisely. Again, I'm not a philosopher, but I'll try to do some justice to the fact that some of you are, and state things precisely. And then I'm going to describe its application in three different areas. One is the quantum theory of gravity. The other is the issue of unification, where this other tradition comes to a crisis. And the third is the application to a question of how to extend or modify quantum theory applies to the universe as a whole. And I anticipate I won't have time for all of this, but I'll do as much of this as I have time for. In any case, I want to advertise that these are the three areas in which this other tradition offers alternatives which are intensely understudied by small numbers of people and are worthy of examination. But first, we need definition of what I mean by relationalism. So we start with, if the other tradition ends with the commonplace assumption that we have to live in a world where we can live, this starts with the commonplace observation, which is that the world is very manifold, that is, we happen to live in the universe where there are a large number of entities and a large number of events, which is a very

50:00 important to note because that means that one particle moving in one dimension is not a good model for what you want to do. And what we want to know is how do these large numbers of entities and events in the history of the universe get their properties. In an absolute scenario that is in the other Platonic Newtonian tradition, I've already discussed but just to rub it in, there's an internal static entity, the geometry of space and time, which gives to the particles their properties, and we call that the background-in-session approach, a background-dependent approach. The most basic statement of relationalism is there is no background, that is, you are not allowed to define the properties of an entity or an event with respect to some structure Anything which is introduced, which is used to give a property to some entity, must itself be a dynamical entity on equal footing with what you started with. Would you say that finally Einstein was also a relation with Einstein? I'm going to say, yes. When he said there is no space, entity or field. Well, I want to say precisely the sense in which Einstein was, and I'm not going to say that sense. So I'm not Julie Marber or John Stachel. I'm not going to give a scholarly account of what Einstein meant and didn't mean, which is pretty subtle and maybe even slightly confused. Probably Einstein wasn't confused, but his readers are confused. But But I'm going to say what I mean by it, which, okay? Okay. So, I already said this, the relational view posits that the fundamental properties of elementary entities consist entirely in relationships between those entities. And here's some examples. So we're not talking about something, you know, hard to imagine. A graph is a relational system. The property of this node, a property of a node of a graph

52:30 is its first neighborhood. That is, the graph that you get if you go one step from it and take the subgraph consisting of those nodes. And all the properties of nodes in graphs are demarked or discussed by talking about subgraphs that contain them. What's the list of nodes that this node attaches to is one of its properties. So a graph is a network of relational properties there exhibited to you in time in a picture. Another set system with relational properties partially ordered set. A partially ordered set is a graph, but a graph where the edges are ordered, and between any two nodes, there's either an ordering in one direction or the other, or there is no relation, and ordering is also transitive. So if there's a node here which is connected to this one, and this one is connected to this one, this one is also connected to this one. And this can be used as an abstract description of causality, and often is used in physics. That is, the arrows represent causal processes, in which case this is called sometimes a causal set, with some additional technical assumptions. For example, that there are no closed loops. And again, it's a list of relations where the properties of any event in this picture, for example, of a discrete history, are what's the set of events that could have caused it and what's the set of events that it gave rise to. So again, a completely relational entity. There are also partly relational systems, so these have no background. You can also imagine studying the possibilities for closed curves embedded, for sets of closed curves embedded in three-dimensional space, just up to topology. So you don't use the metric properties of three-dimensional space, you just use the topological properties. And then the fact that these two closed curves are

55:00 linked is a relational property, but it depends on some reference to a background that is the topology of three-dimensional space that they're embedded in. So we say, we talk of partly relational properties. And knotting of a curve in three space is a partly relational property linking of curves in free space, etc. And graphs could also be embedded in free space in such a way that you could worry about knotting and linking. Okay. What is time in a relational theory? For most people who study these things and developing, the idea is that these, as models of physics, these are dynamical systems, and time is nothing but changes in the network of relations, and the property, and therefore every time if, for example, you switch the relations in a graph, or you change a graph locally, that's an event. And the properties of time in a given history of such events consists of nothing but their orderings. For example, which events modify regions which have been modified by previous events. So, those four things that I call R0 and R4 define what, for most of us physicists who work on fundamental theories of space-time, we mean by saying that our theories are relational. Relationalism can also be considered as a research strategy in which you seek to make progress in whatever it is domain that you work in by seeking to identify structures that play the role of a background and remove them and replace them with relations between dynamical physical entities which allow the current dynamical laws, thus it is hoped increasing the adequacy and the precision of the explanation. That is, you can argue that every time you refer to a background you are explaining something in your dynamical system in terms of something that then you can't ask about. Why is the geometry of space the way it is? It just is the way it is. And by making a relational move,

57:30 you increase the adequacy of your explaining, of your explanations. And this is a strategy, and in this talk, this is all I'm going to say about this, but I have much more to say about this, for example, a talk on Monday at the London School of Dynamics. This is a strategy other areas, for example, in social, political theory, for example, in the work of political philosophers like Roberto Angra, one sees precisely this move being made in which things that are, have no dynamical content and are just posited that are supposed to explain, for example, the rights of an individual are removed and one seeks a better explanation by replacing them with entities or structures that are themselves dynamical. So this goes beyond physics, but that's all I'm going to say about that in this form. Excuse me, is that relational strategy very different from what we call effective theories? It's sort of the reverse, if you like, of the strategy to make effective theories. of relationalism according to a physicist, and now in the time that I have, the few minutes that I have, I'm going to talk about some examples. So, now the answer to your question. So, general relativity is a partly relational theory, which is why I introduced the terminology. In the layers of structure, what do you have to do to produce a description of a space-time in general relativity. You give the dimension of the world, you give the topology of the world, and you give the differential structure. Up to this point, this gives you a manifold of some dimension and topology, say S3 cross R, with the only differential structure that it can have. On top of that, you put some dynamical fields, including the metric fields. In general relativity, all this structure that I call M, the manifold, up to the differential structure, is fixed and is background structure. That's why general relativity is only a part of the relational theory. But the metric and the fields describe relational information. Now, that's not obvious when you first approach general relativity.

1:00:00 It's not obvious from the things that Einstein wrote, although I think he would have agreed with the implications of this, again I'm not a scholar. It's certainly far from obvious in the textbooks, at least the textbooks that I read, and it's really been the work of the people I mentioned, Stasho, Barber, and others, sort of elucidated the fact that these fields have relational information, that all the fields in general information, and here's the key point that Einstein did know, that a physical space-time is not modeled by these structures, by a manifold plus metric plus field, but by an equivalence class of these structures, where any two, you fix the dimension, topology, and differential structure, and then you consider equivalence classes of metrics and fields related by diphenomorphisms of the manifold. And any two metrics and fields on the manifold, which can be taken to each other under a diphtymorphism of that manifold, are identified physically. And this is not a symmetry, and this is why I made the distinction at the very beginning of the talk. This is a physical equivalence. They are mathematically distinct, but physically identified histories of the universe. And that's the key point. That the physical information, the conjecture that relates, or the hypothesis that relates the mathematical structure to a physical history of space-time is not manifold metrics and fields are a physical space-time, but manifolds, metrics, and fields modded out by an infinite equivalence class, an infinite dimensional equivalence class of diphtymorphisms of the manifold correspond to a physical space. What information is coded in the equivalence causes? That is, why wouldn't we like to have a description of general relativity and its dynamics directly in terms of the equivalence causes? That's what we would really like. We don't have it. Why don't we have it is a very interesting question.

1:02:30 But we don't have it. So if some works get at what is the physical information that's coded in the equivalence process, what is it? It's not the values of fields at points, because the only way you can identify, since the diphtymorphisms can take a point to any point, the physical information is not in the value of fields at any point. It's in what's preserved in the relationships between values of fields at points when you move them around under the diffeomorphisms. And that turns out that all the information in the metric that's invariant under the diffeomorphisms is in two structures. The causal structure, i.e., which events are causally related to which, that is, the structure of the light cones of the manifold are taken along by the diffeomorphisms, and the measure, that is the volume element, say for example, if you choose two events and you consider this future light cone intersected this past light cone, that's a set which will have a finite space-time volume under the metric, and under a diffeomorphism it's taken to another set, which however has the same space-time volume. So the causal structure and the measures or volumes of sets defined by the causal structure is the physical information in the space-time. So the causal structure is certainly about relationships, and the volume also, if you like, is about relationships. It's about, roughly speaking, you know, how much can happen between one event and another event. And that can be said more precisely, but I'll go on. Okay? Now, so that's what I have to say about general relativity. And the route in which people, and if you'll excuse me to say it this way, got confused. because they go through Mach, and then they get worried about whether general relativity is Machian or not, and it's very confusing because Mach said five different things, and when Einstein called Machian, there's nowhere to be found in Mach, and it's a big, confused situation, and if you just go through the word, the category of relationalism,

1:05:00 following Barber, this is all following Julian Barber, it's pretty clear. Okay, so now we come to quantum gravity in those, what, I have ten minutes? Okay. And there have been two approaches to quantum gravity, as I said, the background-dependent and the background-independent. We already talked about the fate of the background-dependent approach to quantum gravity, the best version of which is string theory and which has many beautiful developments that come from it, but unfortunately leads to crisis. What's the alternative? So, in the ten minutes, I'll tell you about a few of the alternatives. So, the purists, the analog in this field are the Trotskyists, who follow a pure ideology, actually I have an idea of that, that's what my grandmother said, are people who study what's called causal sex. And what these people say, this is Raphael Sorgian, and others, is that fundamentally the quantum world should be discrete, so if the relations in general relativity are just causal relations, imagine a discrete set of events on which there is no relations but causal relations. So imagine a partially ordered set as a model of the world, and your quantum theory is to which gives an amplitude for every causal set, and that is to be the theory of the world. A quantum space-time history is nothing but a causal set. The dynamics is given by a rule that assigns a quantum amplitude complex number to each history, and then you do some sum over histories kind of quantization. its motivation is that given a classical space-time and there are more words here but let me just talk, the idea is very simple given a classical space-time if you pick randomly some events and write down their causal relations you get a causal set therefore there's a sense in which a causal set can give a discrete approximation excuse me, to a classical space-time So that's sort of the motivating idea. But there's a problem which is the inverse problem, as we call it.

1:07:30 Every classical spacetime can be approximated by a causal set, in fact, in many ways, but almost no partially ordered set is an approximation of any classical spacetime geometry. So it's very easy to go from the classical world to the quantum world, but that's not what we're supposed to be doing. We're supposed to be inventing a fundamental theory with some fundamental dynamics that when you solve it, you get back to the world which is actually big and where the space-time geometry is classical to a good approximation, and nobody ever figured out a way to do that in spite of about 25 years of work here. but why to require that every coson set should give space-time because, for instance, in quantum physics, not all quantum states can be described like particles. That's a very plausible thing to say. Let's just say that no dynamics has ever been invented such that there is something like a low-energy approximation, we were discussing that, or some way in which, quote, classical space-time emerges. and it's sort of an entropy problem there are just way too many discrete entities ones that if you have a large causal set that approximates classical space time you can just add one relation which screws it all up and so the number of ways to do that is the square of the volume of the history of the universe in Planck units So this is in fact an example of a more general problem, called the more generally, in which in many of the approaches to quantum gravity which are background independent, I didn't say the background independent route was easy, even if I'm arguing that it's right. And this catastrophe, something, you know, I have no desire to hide anything, this catastrophe many other research programs, or several other research programs. In general, it's easy to approximate smooth fields with discrete structures. It's very hard to invent a dynamics that picks out those discrete structures that are well approximated by smooth structures.

1:10:00 Okay. New Punta Gravity is the most developed of these background-independence approaches. You have a big school here in France of it, mostly in Marseille, but also elsewhere. and so I don't have to spend too much time on it, and maybe in fact what I'll do if you'll let me is sort of skip, give you the basic picture, and give you an entree into the talk on Friday. The basic talk on Friday will be about some ideas, actually not of myself, about how to deal, how to address this inverse problem in the context of loop quantum gravity. So let me give you the picture and then I'll just say the words as a preview and then I think it will be done. So it turns out that loop quantum gravity combines different kinds of relational structures that I talked about before which is why I chose those to exhibit. So the way that you pick out is you pick first an algebra, like a Lie algebra, or a quantum group, or a supersymmetric Lie algebra, and then you have a space of states which are defined the following way. Oh, the other order, you pick an algebra, and you pick a differentiable manifold. So it's just as partially background independent as general relativity. You pick the same background structure, a dimension, a topology, and a differential structure of the manifold. The differential structure is not very crucial, but for fairness, for completion, we'll mention it. And then there's a space of states defined in the following way. Consider a graph and label the edges of the graph with representations of the algebra, and whenever the edges come together in a node, you take the product of those representations and you choose an invariant, and you label the node with that. such a graph so labeled is called the spin network because they were first defined with the group SU2 and with the edges therefore being labeled by spins by Roger Penrose in the early 1960s

1:12:30 and then consider any embedding of any such graph in your spatial manifold and that provides an orthonormal basis so the Hilbert space of the theory is given by specifying the basis is every embedding up to the morphisms of every such label graph. Now, it's a theorem that I'm skipping because I would have to take 15 minutes to define the terms that a very large class of background independent classical theories of gravity including general relativity have this Hilbert space as their quantization for some choice of algebra G. The dynamics is given by giving a set of local moves, and here are just some examples of them. These are local moves among three-veiling graphs, and these are local moves among four-veiling graphs. All of these graphs have labels coming from the group representation theory, and the dynamics is given by giving an amplitude to each of those local moves. And then a history is a sequence of those local moves, and it has an amplitude, have some over history's quantum theory. So that's what quantum space-time looks like according to quantum gravity. Now, this also has this inverse problem. And the two developments, which I'll talk about on Friday, address the inverse problem in two different ways. One aspect, and again I want to emphasize that this, I had a little bit to do with the applications of these ideas, but these are not my ideas. The first is that in three dimensions, which is where we happen to live, apparently, and only three dimensions of space, there's a huge degeneracy, because given any graph, three-dimensional space in an infinite number of ways, because you can imagine taking the edges and knotting them and braiding them. And these correspond to distinct states. And

1:15:00 since about 1988, we have been confused about what that meant, and that's been part of this inverse problem of going from the quantum geometry to the classical geometry, what to do about the knotting and braiding of these edges. So what I'll describe on Friday, first of all, is work of Fotini-Margopoulou and David Cripps in which they show using techniques from quantum information theory that there are what are called noiseless subsystems or persistent states trapped in the knotting and the braiding. That is, roughly speaking, there are persistent excitations where quantum information is coded in the amplitudes on the different knotted and braided states, and these persist under the evolution rules, thereby giving rise to emergent excitations, which might be elementary particles. and the little bit that I had to do with is an adventurous identification of the simplest of those identifications with real model developmental particles. So that's the first piece of news. And the second piece of news is that even when you do that even under the best expectations for getting a coincidence between classical geometry and quantum geometry There is disorder in the notion of locality, that is you end up with a notion of a ground state where there's a non-zero but very small amplitude for two points in space far away on the point of view of the classical method to be connected to each other. And so we call this disorders or dislocations of locality arising in the process of the classical limit. And these are characteristic effects or generic effects of there being an underlying quantum geometry. And the interesting thing is that since the Planck scale is so small, it's remarkably hard to see these. And under natural assumptions, they only show up at cosmological scales. And I'll leave for Friday what kind of effects they can have at cosmological scales.

1:17:30 So in other words, the matching between notions of locality in the classical approximate geometry and the underlying fundamental part of geometry does not have to be one-to-one. There can be dislocations in locality. The recognition that this must be true comes out of the same work that I mentioned using quantum information theory. And the interesting thing is that it can be exploited to give interesting, large-scale cosmological effects, possibly addressing some of the cosmological puzzles. Okay, let me sum up, because I've said a lot. There are two traditions in the search for a fundamental theory of space, time, matter, etc. And what's remarkable is that both traditions are rich historically, and both traditions have current-day examples, or avatars. And unconsciously or unknowingly, a kind of debate has formed in the theoretical physics world about, and the terms in which we generally debate it are, you know, string theory versus lupon and gravity or background-dependent approaches versus background-independent approaches. But what I'm arguing here is that what we're doing in this debate is nothing but parroting sides of arguments that accommodations like Leibniz and Clark and Newton had amongst themselves hundreds of years ago, each tradition has certainly been, I'm not here to advocate one tradition versus another, each tradition has certainly been in its time extremely fruitful for science. And I'm not trying to make a philosophical distinction between them. What I am trying to do is claim that the current crises connected with predominantly string theory and the string theory landscape and the crisis of predictability and so forth can be understood as consequences of the tradition that it reflects and that it may be, I'm not finding is,

1:20:00 But maybe that the alternative tradition and the approaches to physics that turn out to have to do with or express the alternative tradition may offer hopeful alternatives to that crisis. And I'll stop there. Thank you. and I know it's very hot in here I'm very happy for any discussion yeah let's start I have to first question concerns relational properties or elementary entities consist in talent or relationship elementary entities. And actually, what is the elementary entity in that context? I think it's kind of a difficult question, because if, just coming to the beginning of your talk, you mentioned the Leibniz, so I didn't turn this term, right, that we obliged to treat as entities exactly those which have equal properties, right, so it's become kind of No, no, no. So if I can anticipate, you're quite right. The picking out of what are the elementary entities from contemporary theories is non-trivial. And the reason it's non-trivial is that they're hidden behind a lot of gauge invariance. That's what the diphtymorphism invariance is. The diphtymorphism invariance of general relativity makes it hard to see what the theory is really about. But the same thing is true in Yang-Mill's theory, in quantum A. Mill's theory turns out to be about non-local observables such as Wilson loops. People don't know what these are and I'm happy to explain. But they have to do with parallel transport of degrees of freedom around closed loops. And the analysis, the understanding that quantum gauge theory is not about the field A at points, it's not about the curvature or the field strength that points what are the physical degrees of freedom of the theory is about are about relationships between closed loops and indeed networks that describe parallel transport

1:22:30 is a non-trivial realization that took Boole and Parisi and Mandelstam and Paliikov and Wilson and many people to develop. And the interesting question An interesting question is, why is it so hard to express the field theories we use in terms of elementary identities? Why is the physics hidden in all these piles of gauge invariants? A and B, is it possible that quantum mechanically it's simpler? That is, quantum mechanically, it's reasons that are quite interesting. It's possible to do something we can't do classically, which is to go down to a language of description in terms of the elementary identity. Because that's what we claim these graphs are in the case of quantum general relativity. And the same analysis in classical general relativity yields some big quotient of all of these huge infinite dimensional things, quotient of all these other huge infinite dimensional things. And it's actually possible to compute the quotient in quantum theory. Yeah, actually, my second question exactly comes on that, because when you say in general relativity we define things up to diffeomorphism, and you mean up to reversible diffeomorphism, like isomorphism, right? Because otherwise we wouldn't have anything like equivalence relation. Sure, absolutely. And I just wonder, how to say, kind of nature of this, probably could we go further and just give up this kind of reversibility? Well, you want a group, but there are a lot of things that could be given up. Let's have a technical discussion later. The different ones have to be... Yeah. My question was related. If you think about two differential manifolds, which are without switch on it, which are related by different models, there are, in some sense, the same differential manifolds, which means that if you have two circles through the same radius, they are the same circle. that two differential manifolds without structure are different are different morphic this is a equivalent this is a mathematical triviality but here we have a differential manifolds with some structure names which is the metric and the various fields but i wonder if in this case

1:25:00 this is not a logical triviality i give an example if we want to describe for instance the surface of the Sun. We will see the surface of the Sun, we describe it as a surface with some field on it, like the cooler, the temperature, the magnetic field, what you want. And if you change the description, making a deformer field on the surface, and changing also all the fields, like in relativity you change the metric, you will have always the same description Exactly. So, for me, in any geometrical description of a physical system, the difvermorphism invariance, you have to transport in the difvermorphism also positive, should be a triviality. Are you agree with that? It should be, but it's often... You agree with me, maybe? Well, it depends on what you mean by triviality. So, I mean, for example... I think you can have no correct geometrical description of a physical system if it is not deformable piece invariant in this sense, which is the sense in general. You know, let me just mention a fact which keeps me up nice at some time. Even if we limit ourselves to some very strictly defined mathematical thing like everything is analytic, And I ask you, is there an effective procedure to tell me whether up to a certain precision, two metrics are related by diptymorphism or not? The answer is no. So, what are the things that... In principle, there is. There is a proposition by Carton, which gives a test. and in fact you have to make an infinity of checking but that's the point you have to make an infinity now there are smooth fields you have to make an infinity of checking but even let me make a simpler thing if I give you two graphs embedded in three space up to different morphisms is there a finite procedure that's only polynomial in the number of nodes of the graph tell if they're diphenomorphic or not, if the embeddings are diphenomorphic or even just homomorphic or not. The answer is no, as far as it's known. And that's worrying

1:27:30 if this is supposed to be a fundamental quantum theory. Now, I'm advocating this theory, but this is a worrying part of it, because it says that if you have some procedure, you know, if you're taking the inner product between two states, it may take an infinite to compute me in a product between two states, there are rules. Yes, but I think this is not the point, so we will continue with that. Anyway, we can continue with it. Next is Greedo. I was wondering about the role of symmetries within a relational approach, because of course in a relational approach if you apply the symmetry to the whole universe, So that makes no sense. But if you apply it to a subsystem, the content of Galileo's relative principle is the physics is the same way that the shape is at rest with respect to the core or is moving. That's something that has a physical content that is about subsystems, about different relations between the systems and the world. So I'm wondering about the role that symmetries do play in the relational framework and, in fact, how much role do they play on top of that if one assumes the background? So, without being coy, that's the core of Friday's talks, because the core of the work of Marco Polo and Krauss is how to identify a background in a kind of relational system, a quantum mechanical system, what is a subsystem, and how precisely to identify symmetries that it transforms under with respect to the rest because that's precisely what you have to do to talk about elementary particles moving in space-time or to talk about a black hole and whether it should be a Schwarzschild quantum black hole or a quantum black hole and that's precisely what they did because analogous problems have to be addressed to build a quantum computer, it turns out. That is identifying subsystems and degrees of freedom that are protected and can propagate for a long time in finite temperature and not decode here.

1:30:00 Yes, I don't see in that exact sense non-commutative geometry is like Mitzel or Rolashner. One of the main achievements of the non-commutative geometry in physics was to find the non-commutative algebra of the standard model and to interpret the Higgs boson in terms of the pure non-commutative component of this algebra. So it is a new mathematical interpretation of the standard model, but it is on the side of the standard model. So I agree with you. Let me tell you the aspect of Dr. Muggeny that is background-independent, or aspires to be background-independent. Among the observers, supposing I gave you a Lorentzian metric on space-time, and I want to give background-independent, well, actually, we don't need this, but I want to give background-independent information about the metric. So one way to do it is to define a vial operator on the space-time, if it's an even-dimensional space-time, and consider the spectrum. For people who don't know, that's the equations of motion that describe a fermion moving on the background space-time, like a neutrino. And find the spectrum of that operator, and the spectrum of that operator is invariant under due to morphisms. And one point of view about non-community of geometry as a route to quantum gravity, not as a route to particle physics, as I understand it, and maybe there are experts here, I don't the little bit I understood it from people that I learned it from, is that you can start with the notion of the spectrum of an operator on a space-time as being background-independent and extend it to the spectrum of an operator in an algebra which is not an algebra of operators on a community of metaphors. And by further attempting to express the dynamics directly in terms of properties of the spectra,

1:32:30 properties of the trace and so forth of the spectra of the operator, you can hope to have a dynamics which is completely dipymorphism invariant and the fundamental dynamics of the space-time geometry. So that's the direction in which it goes. not succeeded in that direction so far, to my understanding. but I accept the criticism, and if I do this talk again, I'll put non-judge on the other side for the time. I think that it is partially relational as a general relativity. Sure. Only partially. Sure. I accept the criticism. Michael? Okay. Different topic, Lee. How do you see the weak and strong versions the relations program? For people who don't know it, so let's first give some background. So a photographic principle is an ambitious attempt at a principle of quantum theory of gravity formulated by Gerard Tope. And the principle, so I'm just going to describe it if people want. the answer is I don't know and I've puzzled over for many years other questions, maybe I should just leave it at that so it wasn't a totally dumb question it wasn't a totally dumb question no, no, no, certainly certainly I and others have struggled to take Pope's ideas there is one thing there is one thing I can spend a little time on, there is a version of it which is pre-Etoft, which was due to Lewis Crane, and became an important idea in quantum gravity and is closely related to topological quantum field theory, which is an important mathematical structure. This was actually what I had in mind. Okay, behind some of these developments, and roughly speaking, the hypothesis would be that there is no, to take more seriously and to say there is no quantum state or space of quantum states for a complete system, that what we actually do when we describe the world

1:35:00 quantum mechanically is we consider a subsystem of the world and attribute quantum states to the subsystem, and a space of quantum states to the subsystem, and an algebra that acts on that space of states, which is generated by some representation of those measurements that a being from external to the system could make. And that was, Lewis Crane proposed a formalization of that, in which he said, roughly speaking, that a quantum theory of gravity would not be an assignment of a quantum state to the universe. It would be an assignment of a Hilbert space for every surface you could put in space dividing the universe into two pieces. So for every way you could imagine dividing the universe into two pieces, there would be an algebra of operators corresponding to information that could flow from one piece to another and a Hilbert space that would represent it. And the conjecture, and this is where it ties to Ettoft and Bekenstein, is that the dimension of that Hilbert space would be given or bounded by in different versions by the exponential of the area of the surface divided by four in Planck units. And this is something which has been developed. It turns out to fit into this beautiful mathematical structure called topological field theories, which are quantum field theories, which have precisely the structure I just described, and which are closely related to a large class of quantum gravity models, including new quantum gravity incident foam model. So it plays some role, but I mean certainly it's an idea that has yet to have its full realization, and many people, including me, are hopeful that there's some very deep way to go from a principle to a mathematical realization of it. I'll say one more question. Thank you. Would you like to say something about the Darwinian perspective you mentioned about its life? Sure, but very briefly, and that's what I'm talking about tomorrow at City Science of...

1:37:30 If the landscape of theories is right, that is, if fundamental physics does not give a theory which is predictive to the universe, but gives a large number of possible theories, then is there an alternative to the anthropic principles? And the idea that was proposed some time ago is that of course there is, because biology faced essentially the same conundrum a long, long time ago, and Darwin found a strategy out for biology, which is that there can be natural processes which populate a landscape of possible creatures or possible ecosystems, which is both explanatory and at times predictive, although often it's hard to tease those predictions out. And what you need is a space of possible configurations, which is a space of possible gene sequences for biology and spaces of parameters of the standard model for particle physics, fundamental physics. You need a mode of reproduction. You need a mode of variety and a mode of selection. So, before we exhaust everybody's patience with the heat, the mode of reproduction that was proposed is creation of new universes through black holes, which black hole singularity is bouncing, which is increasing evidence for recently in recent work of Beaujolais and many other people, Ashtar Khar, other people. So the mode of variety or variation is still invented, that is that one can postulate that the world that would emerge from the singularity of a black hole would have parameters of its particle physics slightly different than the given one, and that's still a priority. There's no justification for that. But given those two things, if you give me those two things, then there's a clear selection

1:40:00 principle, which is that the number of black holes that a universe like ours has, it turns out to be strongly dependent on the parameters of elementary particle physics. It's easy to see that it would change any number of the following constants, the electron mass, the neutron mass, the photon mass, the strengths of any of the forces, weak, strong, electromagnetic interaction, gravity, plus a bunch of other strange cork mass, you change drastically the number of black holes and strongly to plausibly in different cases decrease the number of black holes. So the hypothesis is that we live in a world in which the parameters have been selected by such a process to maximize the production of black holes. So that's the Okay, I'm going to make a last comment before we move, and then, just to go back to the topic of symmetry and close on that maybe. So, it's a question and a comment at the same time. I still want to say the role for symmetry as a tool that supports physical theory in the way, so you, from the very beginning, not to speak about local symmetries and more engaged symmetries, which, if you go back to this and you do that's what you did, in the context of quantum gravity, it refers, again, to identifying subsystems and talking about properties of subsystems, whether it's a physical subsystem or an equally seen subsystem which will not actually survive the subsystem. So, there are two senses in which you talk about symmetries, and the second one, it seems, can be preserved and can indeed be maybe even phrased as something that gives you the way to construct a physical thing, because gauge symmetries are tools for constructing physical And it seems that when Juan Mugabe starts identifying subsystems and looking at properties in one way or another, it may need to go and look at local, but in a different sense, local symmetries.

1:42:30 So it's a comment, yeah. Yeah, it's a comment, I mean, the only thing that, I mean, there's a big thing I can say and a little thing that I can say. Say both. No, they're both the same thing. We're very far from done. And I think that the... So let me turn this into a comment on the relationship between philosophy and physics. The philosophers, and we're not one of them, but philosophers are often exasperating for us physicists because you seem to see your job as kind of codifying what's come before, giving a better understanding of one part of quantum mechanics or special relativity. And often there are important insights that come from that. But if you will, the partnership between physics and philosophy has been much more productive than that in the past. and what people with philosophical training I think are really needed for is to keep prodding us and to keep finding the compromises that we make conceptually because we're, you know, scientists are pragmatists we often, in the heat of trying to do something make compromises, ignore things and let me just give one example, okay there's this really, really funny thing which is that there's an extension of special relativity where there's more than one invariant scale, there's an invariant velocity scale and there's an invariant energy scale or a length scale. This thing has been, there is such, in fact there's a big class of such extensions of special relativity. They have been sitting there since 1905. Why, and so I'm going to say this a little bit provocatively, why no philosopher of physics, and maybe there was one somewhere, didn't stand up and say, wait a minute, I'm going through the principles of special relativity, and there's room for an extension that you guys have never thought of. Why that didn't happen makes me think that philosophers are not being adventurous enough.

1:45:00 Because it's exactly the kind of thing that by thinking carefully over the logical relations principles in special relativity and which means that there's a reason why there's two principles which means that there must be theories where you know one is true when the other is altered and it's that kind of thing that you know if philosophers were not so polite they could help progress move much faster that's my thank you so Lee before we talk could you just say again quite clearly the times and places of your other two talks I don't think everybody caught them I don't actually I don't remember exactly the rule it's in Collège de France at 2 o'clock in the If you want... This is on Friday. Salle 2, Collège de France, dans le grand bâtiment. Et en ce moment, 14h30. Si vous voulez m'envoyer un mail, si vous voulez... Envoyez-moi un mail, M-A-R-C-L-R, D'accord, d'accord, ok. Mais aussi demain, c'est aussi une conférence demain. C'était La Villette, n'est-ce pas? You're speaking at La Villette tomorrow, aren't you as well? that? 9.30 in the morning. In the morning? Yes. And just for half an hour. It's a public talk. Great. I'm not going to say anything there that I haven't said for 10 years. I mean, I might say it's a different place, but... It's a nice place to go to, though. Okay, right. Thanks a lot. The Friday talks... I'm sorry. The Friday talks... I'm going to make interesting questions tomorrow. You got it. And Mark is speaking To what time? At the same place? You got it? No, no, no, no, at I-H-E-S. No, no, no, Boulevard Spayage, she says, if I go to the right. Boulevard Spayage, oh, M-A-S-H, I'm sorry, Maison de Sciences de l'Homme, yes, sorry. So you know how bad I am at catching French pronunciation of initials? M-A-S-H, that's Maison de Sciences de l'Homme, yeah, sure, sure. Well, that's, that's the, that's the, that's the fact of the morning.

1:47:30 If it's in the histoire de géométrie series, which is what I would expect it to be, then those are normally in the morning, isn't it? It's absolutely just a check. Those are normally between 10 and 12, don't you? Those, so there's some of them. Better ask him. Okay. Anyway, it's just, do you know the truth of the matter of the structure?