Why Time is Necessary to Cosmology

0:00 Now, given those postulates, there's an argument, which is roughly violent. This is a configuration space, and this is some nice set of trajectories. And this argument can be given much more carefully than I'm about to give it. then all observables are functions of the trajectories, and since there's no meaning to allow them along the trajectory, the particular trajectory, all you can do is restrict an observation, one of the observations, to restrict yourself to a trajectory. Now, how is it that you could just have an observation which restricts you to a trajectory without knowing what time it is. Well, the postulates say you can't have a measurement which in some absolute sense measures what time it is. The only thing that you can measure is the correlations between things you can observe that you can infer to give you some information about something like a physical clock. In other words, in the variables described by the configuration space are the degrees of freedom that you would look at to look for a clock. And by locating the curve, you could discover not a statement like, it is 5 o'clock, 14 billion years after the Big Bang, but you could discover a statement like, okay, when it is 5 o'clock, 14 billion years after the Big Bang, then if you look around, and a whole long list of other things are true, you're going to see yourself inside of this group. And those kind of statements are functions of the whole trajectory and other points. And you can show that all observables that satisfy these principles must be functions for that time. So therefore, the theory, the things that the observations distinguish is the space of trajectories, not the configuration space. They can just locate you somewhere in this lower dimensional space,

2:30 which is the space of trajectory. But once you have observables that tell you what trajectory you're on, then there's no longer an external time. The trajectory itself has disappeared. You might be able to reconstruct some notion of the trajectory from all the complicated functions on a space of trajectory, or you might not. But the fundamental observables don't know anything about labeling where you are in history, they just label which history you're on. Now that's the classical argument, and the fine mechanical argument is very similar, And maybe rather than putting on that transparency, I'll just say that where it changes is that here, instead of the configuration space, you have a Hilbert space, a finite or interdimensional complex vector space. Here you have conventionally evolution by sub-linear evolution operator. Here you have the postulate that you can make enough measurements ideally to determine a pure state, but practically to determine some mixed state, some density matrix, which is sufficiently interesting. And then that these postulates also hold quantum mechanical, in this quantum mechanical version of saying that both that the theory only knows about correlations between local measurements and doesn't know anything entirely about points, and means that the theory doesn't know anything about labeling a possible trajectory. And roughly speaking, what happens in the quantum mechanical vertical version is that the Schrodinger equation deteriorates, because there's no t, and the Schrodinger equation deteriorates from d dt of the state, is the Hamiltonian on the state, i h bar, and this part simply doesn't mean anything anymore. In fact, the physical requirement is the state can't depend on any external time parameter, which would be a parametrization of the history,

5:00 so therefore, the Hamiltonian on the state is zero. Now, experts know I could have said these things in a more sophisticated way, but I hope that I've said enough to make it clear. Now, as I said, and I'm happy to discuss this later, I think I have stood up in Oxford and many other people have and defended the argument that if you believe something like those postulates, then China is not a fundamental notion in a cosmological theory. And so I'll take that as a given and attack the postulates. And some of the attacks are on the classical versions and some of the attacks are on the prime mechanical versions. But let me just remind you of the postulants again, and I'll bring this back to you too. First, that we can construct the configuration space. Second, that there is either classical or prime mechanical deterministic evolution. Third, that we can observe enough to at least in an average or coarse-grained sense or probabilistic sense to determine what state or trajectory the universe is in. And fourth, that the state is that the observables have only to do with relationships among observable variables, which means that you don't measure fields directly, but only relationships between that are preserved when you move the names of all the points around, and fourth, I'm sorry, fifth, that two trajectories that differ just by changing the name of the kind of parameter are physically identifiable. So now I'm going to attack those. Can I just ask, before you had in a red box two postulates that you seem to endorse. Yes. And they were close to the kind of constructability A and C. And I'm wondering whether A and C, which you would seem to like... No, I'm going to attack primarily A and C. Okay, but what about the ones in the red box then? I'll let you just... Yes, logically, by attacking A and C, I'm attacking the ones in the box.

7:30 Oh, fine. So the red box was a target just as much as you do on the white box. Okay, thank you. I was just going to ask you, why, insofar as we're talking about time, why is postulate being not sufficient in itself to conclude that time is not coming up? Oh, because if I didn't have these others, it would be useless. Supposing I can't define my integration space, then it's useless. And since I'm going to pack it, I thought I'd write it down. Thank you. I'm getting into that, but then the third thing is that that sort of information will only tell us what we should get from Iran. Yes, but I'm... If you're attacking prospects, we're just saying we don't really get to the issue of those... Yes, I will. But at that time, we seem to... It doesn't seem to help, as it were. I mean, then we've got even less than before. Yes, come back after I've done the attack. Anybody have a comment? So sort of five minutes or less for each of four facts. First, some language. So the first one is, can we actually, in a real physical theory, in general relativity, in your strength theory, in your super gravity, in some real theory, not some model, construct enough observables to have a go and realize it. And I want to comment on that, and I want to first say that there are people in cosmology who talk about two kinds of observables, and it's important to the same. First, what I want to call causal observables. There are too many words on transparency. What I mean by a causal observable is one that uses an implicit call to or description of the causal structure, at least in a region, of the observer.

10:00 In other words, in this kind of observable, you say, there is some observer inside the universe, which is carrying a clock, and which you can identify by some means. She has pink hair, red glasses, is on the planet Mars, has a clock, which you can calibrate with cosmic time by some procedure, in some history where you have some reason to believe you might at least approximately be in the space of configurations near that, some region on something like the world line. And then you look past and ask what information comes in. So that's what I mean by a causal observable. Such an observable, of course, corresponds to what we actually observe in the cosmological theory. we observe is sitting on the Earth with our radio telescopes and our satellites and so forth. By the way, I mean, if I don't have to emphasize the background for this talk, I mean, this is an academic philosophical, well, I'm trying to do philosophical talk, but there are claims in the literature frequently that the satellites that measure the cosmic microwave background are constraining quantum periods of gravity. And I'm really addressing the possibility of making such claims. This is no longer science fiction. I mean, there are, they certainly are supposed to constrain strongly inflationary theories, which are about sort of, you know, a few thousand or a few million Tompkins after quote the Big Bang. And there are claims that to get that right, you have to really constrain theories about quantum effects in cosmology. So that's really one of the best. And these are the kinds of literables we use. And let me also note, for people who know what they are in the history formulations, it's easy to construct such a better way. Because part of the formulation has to do with holds based on histories like that, where all this structure is there. Does it matter the difference of there being some kind of functionals of the state of affairs in the upside-down V as against being functionals of the state of affairs in the entire past Mike Code. I'll come to that. I'll come to that. Because I didn't quite know what you said. No, but these kind of observables measure states of affairs in the past Mike Code.

12:30 Okay. That's what we really observe. Okay. Now, what the formalisms in which these arguments arise talk about are a different kind of observables, which are called Hamiltonian constraint observables. And these are observables constructed to make a theory that's within a theory that satisfies the postulates that I laid down. And this is probably the most technical transparency, so I'll go quickly through this. But the problem is that, so let me just say, and if people want to come back to it, that there are several ways within a theory of the kind that I've been discussing where people have tried to construct observables, and to this date, they have not resulted in the construction in a realistic theory of anything which could be construed as an observable that could be measured by an observer in the space-time. There are results about observables in idealized models with one or two degrees of freedom, which are useless for us, and And there are results about, quote, formal observables, which, however, are not measurable. An example would be the largest volume, spatial volume, that the universe can achieve in its history, given one definition of what a surface of simultaneity is. That's not something that is measurable by us directly. Now, maybe, I'm realizing this is probably too technical, but let me just say that every strategy that people have proposed to disrupt observables in this language has so far failed, and I'm prepared to make arguments that those failures are really serious, and if people want, I can come back to those arguments. That would be a talk to be given to physicists. But just to give you a flavor of it, it's related to really what I said at the beginning when I was talking about novelty. That is, if you imagine that the universe has some state at some early time, where it just consists of a very high temperature plasma of elementary particles in some gravitational And you want to construct an observable, which is somehow a function of the data at that time, which is going to tell me what I see when I look through a telescope now, then

15:00 that requires solving and inverting explicitly the equations of motion to take the data after a million years and convert them into the data after 14 billion years. And that is, it requires that we have an explicit solution of the equation of the motion for all possible data at that early time to really do this. And that, in any theory which is not explicitly solvable or technically integrable, is practically speaking impossible. And it's that kind of practical impossibility that I want to question and wonder whether it's actually an issue of principle. that will come out in the next three specials, which are simpler. So, and these are associated with different people. Ted Newman is a relativist. He doesn't remember making this argument, but I remember him about ten years ago making this argument often. The other people do remember making their arguments. And this is the semi-mentioned issue of chaos. So, we don't know whether the field equations for general relativity classically are chaotic. But we know that in the class of reduction, when you cut down degrees of freedom from infinite degrees of freedom to finite degrees of freedom, as soon as you get more than three degrees of freedom, the equation would be chaotic. And an example of that, if people want, is called the Bianchi-9 universe. And anything that contains that, including we think practically anything with spatial inhomogeneity, has chaotic behavior. So it's likely, but not proven, and of course it's not even fully formulated because it's a theory of significant number of degrees of freedom, that in some sense general relativity is chaotic. Now, what that means, that it's chaotic, is roughly speaking that if you have the configuration space, you have some events on the configuration space, and it has some open sets around it, then every trajectory, given the trajectory, comes within each open set. Every trajectory which comes within each open set surrounding every event. That's the definition, I think, of your diversity, your ergodicity, which is satisfied by these deductions of general relativity and therefore, presumably, by general relativity itself.

17:30 Now, that's okay for standard chaotic theory, but now let me add the restraint that in general relativity, the observables are supposed to be functions not in the configuration space, but in the trajectories. By now I see some function on the space that is constant along the trajectories. But every trajectory comes into every open set. Therefore, such a function is not going to have any differentiable behavior in the name of any point. And therefore, the things that we like to do to describe classical dynamical theories, like writing down Poisson brackets, that is not a rigorous argument, but it's not clear that you could find Poisson brackets. And if you can't define a Poisson bracket, you can't ask questions like, what's the algebra of observables, or which observables commute with which symmetries of the theory. So, Fred Newman used to worry. It may be that if gender relativity is chaotic, it has no observables in a formal sense. And I don't know the answer to that when I'm presenting this series of worries. The second worry is due to Plotini-Marco And I think she discussed this here, last year, and you were alluding to it earlier. So, her point is that in any realistic cosmology, and one can see this even in the models, I thought in the Marks and Walker models, where the universe is spatially compact, generic observers past light cones do not intersect all of the Cauchy surface. I forgot to say where the Cauchy surface is. Cauchy surface is some space-like surface on which, which has the property that every causal null or timeline worldwide intersects it somewhere. So you can get data on it and evolve it to the future. It's a full spatial slide. So no observer sees in the past white cone all of the Cauchy surface. say this one, Q, are in the position that there is information about the universe that they cannot obtain by any measurement they make, but if they wait longer, say so they

20:00 would ask, they will obtain it. But that's always true. Until, unless you're the observer at the final singularity, which turns out. So, what that means is that in any coarse which just doesn't assume that the stuff that you can't see is like the stuff that you can't see, that doesn't assume spatial homogeneity, you cannot measure enough observable to determine what trajectory you're on. Now, as no internal observer can determine in any coarse-grained sense, short of the extreme coarse-graining of complete homogeneity, what trajectory you're on. Now, she goes on and draws some implications from this, which are that a logic of the observable is in some sense an intuitionistic or a topos logic, but I don't need that in this discussion. But this program is actually really interesting to represent. This is enough to have this And remember, the theme here is I'm not interested in cosmology as some being outside the universe might do it. I'm not interested in theology. I'm not interested in making a universe in my backyard shack. I'm interested in doing cosmology about the universe in which I find myself in, and this seems to be a significant limitation. And that's Constitut C. Now, I'm going to pass Constitut A, and I call this Stu Kaufman's argument. He actually has made and investigated this argument or analyzed this argument in the context of theoretical biology and economics. But in discussion, we realized that it might are inclined also to general relativity and quantum gravity. So I'll just give the argument straight. So first of all, as I said, in general relativity, the configuration space is constructed, quote, is described in the following way. You take some manifold, a three-dimensional manifold, you have on it the space of possible metrics as a function to measure, determine the geometry on the manifold.

22:30 However, and possibly some other fields, electromagnetic fields, neutrino fields, whatever you have. However, that manifold plus the geometry, which is the metric plus the fields, is not a model for the configuration of the universe. A model for the configuration of the universe is that modded out not by any demorphism of that manifold, by any map that takes the points of the manifolds to other points of the manifolds in any way that deserves only smoother functions. We don't care about the functions. What's physically meaningful is only the correlations which are preserved under those maps. So, and if people want, I mean there's good technical arguments, by the way, that this is really true. This is really what generalities have, and I'm skipping those arguments that people want that we give them. Now, so this is what we need to do to construct a configuration space. Now, nobody actually knows how to do that. That is, the quotient of an infinite dimensional space by a very complicated infinite dimensional group, we know very little about. We know the dimensions about it, but we know very little about it. And there is certainly no finite procedure known for, for example, if If I give you two metrics, a metric is a collection of six functions in some coordinate system. If I even fix the coordinate system and give you two metrics on the same metaphode, and you tell me whether or not there is any rule in fact, and we know if there is no finite procedure for doing that, it's known. And if there is no finite procedure, then we don't need no finite procedure for constructing quotient. Now, so we don't know that object exists. That's the final problem. Now, there's an analog quantum mechanical problem, which is very close to it. Quantum mechanically, the configurations are embedded in the straight manifold of some labeled graph, which is called the spin network. And this is true in general relativity, in supergravity, in general relativity of supergravity coupled to any physical fields that you'd like. It's true in a large class of theories.

25:00 However, again, the physical state, and in fact the orthonormal states of the community correspond not to the embedding of that graph into the spatial manifold, but to the equivalence classes of those, up to, again, these 50 morphisms. And so the question is, is there a presentation of these classes that allows you to count them, or label them? And the answer is no. There is no known finite procedure. For example, if I give you two embedded graphs, say in There's no finite procedure known to tell whether they are in fact related by some epimorphism or not. Now, if the graph is actually a single knot, then it's a recent result, at least I think in the last ten years or so, that there is a finite procedure and it's related to the classification of a certain kind of finite group. And that's considered a big result in topology. But for graphs with intersections, it's not known whether you can use it. If you can do it, then you can't do any of the things that you can mention in the product mechanics, like take the inner product between two states. Because when you take the inner product between two states, you have to sum over the basis elements. And if in any presentation it's known, you can't tell whether when you come to some presentation element, it might be earlier in the list, you can't know that you've constructed, you computed the inner product correctly. You can't do quantum mechanics, you can't construct the inner product, you can't do quantum mechanics. Now... Sorry, this quotient thing is by diphtheomorphism, called the spatial manifold, not just by automorphism of the graph. Yes, oh yes. Okay. Now, again, remember, I actually require something not even so strong. I require not just there would be some finite procedure, but there would be a procedure that could be carried out by a computer in my past light cone. And even the solution known for knots, the time required to classify the knots grows like some high power of the number of nodes of the projection of the knot on some surface.

27:30 So, here my postulates A and B are in danger of failing. Okay, so that's the last attack. And that's attacking even the notion, either classically the different configuration space or quantum mechanically, that there can be a state space with a well-defined inner product. Now, conclusions. First, so far nobody has been able to construct would be a procedure for constructing observables to make sense of a cosmological theory of the kind that would be required to flesh out the postulants that I started with. Second, there are three good arguments that this may never be possible for a new theory, which I've just given. Now, let me go back to what I was doing when I introduced the problem of observables. I said there were two kinds of observables. Those that make explicit reference to an observer inside the universe having some kind of time and looking into a vast life cone. I call those causal observables. And those are the ones that we know how to measure, and those are the ones in a history formulation where the data is the whole history of the universe, so we know how to describe. I have not attacked that notion of the observable, I've attacked the notions of the observable that have to do with the formulations of the theories in which time disappears, in which all observables become not functions on the trajectories or on the configuration space, but just functions of the space of trajectories. And in fact, that notion of observable, which comes about by trying to realize what's called a Hamiltonian or canonical formulation of the theory, either classically or unmechanically. Now, if that second kind of observable can't deconstructed, that leaves the first kind of observable, which are in any case the things that we observe.

30:00 Now, that leads me tentatively, of course, because the stuff is of course really hard, but it leads at least to my kind of belief, is that that tells me that first causal structure, that is the structure of the history of causality, one of the past white cones, is real, not just an artifact of the classical, there are many people who say that the space-time, there are many people who say something like, just like the trajectory of an electron, which is real in a classical dynamic, becomes not real in quantum dynamics of an electron, it's just remaining the wave function, the history of a space-time, including relations like causality, which are real in classical general relativity, become not real in quantum gravity, of quantum typology, which just gives you some amplitude, probability amplitude for spaces of configurations. The notions of observables which seem to be required to make sense of such a theory seem to be problematic, so therefore maybe we have to turn around and believe that the causal structure must be real and must therefore be really defined quantum mechanically. However, this causal structure itself is, if the causal structure is real, we're done. Because the structure of causality of the past events is a notion of time. And it's a notion of time that gives us, one might imagine, all that we need to say that time is real, and to have a notion of time in a pathological theory. So we, so if we have to use observables and make use of notions like looking down the past life tone, then we have to make use of causal structure. So we have to have a theory where causal structure is fundamental and doesn't go away quantum mechanically. But then, the causal structure gives us, in each history, classical or quantum mechanical, a notion of time, which is related to what we observe in fact. And then there are these interesting comments that you have to get this kind of multi-observer structure in which different observers at different times looking back, different times defined by causality, looking back on a path-wise mode can give two times differently to different compositions. So that's where I stand, and I want to end with a provocative point, really just based

32:30 on the last remark coming from the argument I'm calling school countenance argument. Which is, what do we do? Calling that argument is really right. What do we do if we're trying to describe a dynamical system, i.e. the universe we live in, and the configuration space that we can write down and describe in words, it's not actually constructible. How do we do dynamics? How do we do physics without a configuration space? Without having a pre-specified space of all the possible configurations? Well, we can do it if we restrict, frankly, if we change and restrict what we mean by dynamics. If we're willing to say this, and I would draw something, you know, say some graph here, is the present configuration for the information I have about the present, oh, sorry, about the present configuration, about the present configuration, I can't iterate the whole space of configurations, but maybe I can write down all that I'm able to observe from observing problem of what the configuration is immediately prior to me. And maybe it's something which is open because there is information that goes outside my past life mode. And maybe what theory can do, if it can construct a complete configuration space, is it can tell me what are the next possible configurations? What are the possible configurations that are one quantum transition away from those configurations? And Stuart Kauffman has a that in the context of biology, it's called the adjacent possible. The configurations that are one step away. And if you can iterate the configurations one step away, you can have a probability, a theory that gives you a probability amplitude for different ways to jump one step away. And maybe that is sufficient to define a dynamical theory. And, but we would again note that in such a theory, the notion of evolution, and hence the notion of time, based on causality, is intrinsic to the dynamics of the theory.

35:00 You're never going to get rid of time in such a theory. So, let me close by saying that there's been an argument over the last, I don't know, 40-something, 50 years, that in a fundamental theory of quantum gravity or cosmology, time would go away, and there would be no fundamental notion of time. And the argument that I'm making, which is of course just an argument, it's not a theorem, is that so far that program of constructing a complete quantum theory of cosmology, or even a classical theory of cosmology, in which there is no intrinsic notion of time, has failed on the details. And the reason for my two postulates in the beginning is I want push the possibility that that failure on the details is a failure in principle, because we're not sufficiently taking into account the fact that any physical theory must be constructable by us observers in the universe, and must be calculable by observers here in the universe, and testable by observers here in the universe. And if we make those, if we elevate that idea to a principle, then what may be issues of practicality, i.e., the calculation is doable but requires a huge number of steps to the computer, become questions of principle. And those questions of principle may be enough to knock us back to a universe in which time has a real existence, and that time is closely related to the causal structure that we see when we look around and look at a past life. So I'll start with that. That was actually fascinating. But it seemed to me there was a certain ambiguity about what you were saying. Now, it may well be that a lot of the things that are supposed to figure in the theory aren't calculable by us. But on the other hand, the fact that they aren't calculable by us

37:30 doesn't seem to mean that they're not, as it were, out there as part of reality. And I wasn't sure which of two things you were saying. to some extent anti-realist, in other words, but one should be content with a theory which simply, as it were, encompasses what we are actually able to calculate, in any way, in principle. But it seems to me, and some people might say, well, that's all the theory is anyway. But I think there's a certain inclination to say, well, just because we can't calculate it doesn't mean it is there, we still want a realist view of the world. We want, in a way, to have some sense as to how God perceives it. Do you see what I mean? And there may be lots of things in God's vision which are beyond our powers of calculating, but nevertheless, it seems to me that it's an important issue whether or not they are really there. I mean, are you a realist about the universe? So are you, do you have a view of physics, which is sort of the equivalent in mathematical, in mathematics, or say, intuitionism? So, are you a realist? So, I would like to think that I'm a realist, but I am of a state of mind where realism is in contradiction with the notion that this has nothing to do with theology. this has to do with what I think is the insipid use of appeals to theology inside of physical theory. Let me make that clear. But I think that the kind of statement that he made is a use of a theological notion which has no place in the kind of physical theory that I would find interesting. The point, and this is between Dr. Kupula's point, which I think is a very strong point. When we do general relativity, we draw these pictures on our blackboard. We go and we draw a picture and we say, this is the space-time. And I just have to put some singularity in it, put some conformal boundary, put a few more things. And people say, that's a picture of the space-time. And what I'm saying is that that notion that you can have a picture of a space-time as if you're outside of it is deeply misleading.

40:00 And we only fall into it because of the history from theology that came in and confused physicists in past generations between doing science and making construction of what God would see if God looked at the universe. The kind of physical theory, the kind of physical theory I want to discuss and I could believe in, the only thing that you can draw a picture of is what one of these observers will see inside the universe. Now, the interesting property of real universe is that there's no internal observer, There's no observer inside the universe who can give the truth value to every proposition about the universe given, but there is some observer who can give the truth value to the proposition, to every proposition. For every proposition, well, no, for many propositions, there will be some observer who can give it. There may also be some propositions that no observer can give the truth value to. Like, if you draw a surface roughly 14 billion years after the Big Bang, there are exactly 370 billion cats in the universe. It may mean that there is no observer, ever, in a position to give that statement the truth value. And I think that this is significant, and this really puts me in point, and this is why I find very interesting kinds of things that Jeremy and Christian have been thinking about and finding non-standard logic related to intuitionism to physical theory. The thing that for me is the motivation. This is what I find most interesting about what they are doing. Because it may be that cosmological theory has to be able to deal with the fact that the observable fact, because it seems to be true of the universe we've given, that there is no universal observer who can do the truth by anything. But that doesn't mean it can't have a coherent mathematical formulation. There's quite a few, my friend. So, I'll try... If that's all right, no, you keep the answers hard, but my question may come back in other forms. I'm going to suggest that we are all sort of zooming along without having to come back.

42:30 So it's Simon and then Oliver and then Harvey and then Leib and then several other people. I think that's how I'll start. I think that's how I'll start with that. It's a long way to find it because the reader has seen, one of the two points, one is the reader has seen as you were saying, look, the traditional perception we have in classical presumes so let's take note of the theory which does not presume and then there's a dot, dot, dot, something to follow from that. And the one thing with both the magic systems is surely we don't have a theory when you could say that computation we're building that much in. The one thing we would have a theory is that somehow give us proof. Give us clues to the natural reality the magic questions. Why on earth should we have? That by taking note of our limitations So, two points. One of them is, I'm not saying that our limitations are in contradiction with general relativity and towards formalization. I'm saying that in contradiction with a particular attemptive, but I can fail formulation of general relativity in terms of, quote, this the timeless picture. I think that the timeless picture is a fake. That is, it's good for some models with a small number to do the freedom, but there's no there there. There's no procedure that anybody knows how to carry out to actually do any work of any interest with those, without attempt to formulate a new theory. And part of my ideas is to call attention to that. General relativity has, in their field equations, they describe space-time as some space, whether

45:00 I don't know what notion of truth that you're referring to, and I'm pretty naive. I know, I mean, I'm pretty naive, as you know, trying to think about things like that. So what I'm really looking for is some notion of truth which is useful given our limitations. And I find it interesting to think about that. And in particular, what I find interesting about this kind of structure for truth, that, is that there can be propositions whose truth value, whether you can give a true or false truth value to them depends on where you are in the history of the universe. It means that there's a kind of time dependence to logic. And even a causal structure of dependence to logic that I find fascinating. And I think that there could be a positive development from that. If I was much more sophisticated and spent more time thinking about it, I might have something to say about the relationship with this relationship with philosophy, mathematics, etc. But many of you know much more about that than I do. I think I have a second question. I think I should Is that all right? You're a bit in the queue here. Yeah, yeah. All of them. Now you're the same. I'll ask you a question. Yes, sir. It's about the new one. Okay. I mean, surely there are some solutions. in this sense was something like maximum size of the universal reach. Now surely there are going to be open sets in this configuration space which only contain configurations involving the universal being larger than a certain size. I'm not sure, but let me give you that. I don't know what that's true, but that's what I'm thinking about.

47:30 You might think that in the sort of full, not in the normal case, but in the full case, you will have solutions that fill equations by the universe that doesn't get beyond certain And any trajectory representing such a university is going to go near a region of the configuration space, which holds the university much, much larger. Let me show you something. Let me show you how to think about the D&T 9 model. The way to think about the D&T 9 model is to think that there are three walls. This is true to a very good approximation, where down these channels, if you go infinitely – so we're in a two-dimensional configuration space – and down these channels, if you go infinitely far, they meet. So they meet in the same direction. And as cosmic time goes on, the area within the walls is growing. It doesn't matter. They're a kind of potential in a certain reduction of the field of pressure. These are universes which are spatial and homogeneous, but anisocaptic to make the most general one. And in configuration, there's a little wall which is bouncing. That's what they look like. And so it's like billiards with these channels on a billiard table, which is slowly expanding. Now what it means is that as you go, and then at some point it comes to a map, so imagine you're going into the future singularity. you're coming up, you're going into the background of the past singularity, you can show that in between your present state and when the area shrinks to zero, which is the singularity, having time zero, the thing will bounce an infinite number of times off of some wall. So no matter how close you are in some physical time variable, to quote the beginning, there comes to an infinite number of bounces before you get there. Now, define for us non-observables, which are functions of the trajectory of the non-desert

50:00 configuration, because any observable can't formally depend on where you are on the trajectory. And even in this simple case on the plane, nobody saw it. Do you mean an infinite number of bounces in each of the three channels? Ah, right. Because otherwise, an observable could be, I'm always in the top left channel. throughout my life. That would be... I don't know the answer. What is it that's balancing if you're trying to translate it? These two axes are the metric, which is the 3x3 matrix. This is x and this is y. The metric looks something like x, y, and then there's some function of x and y in the third one. So there are two of the three diagonal components of the metric. They tell you how much things are stretched in two of the directions. So the universe is doing a lot of this as it's getting near the initial refinance. It's doing a lot of shearing. It's doing infinitely much shearing. Okay, so all we're going to do in the queue is the second question. Maybe it would be helpful at this stage. I'm a little bit confused about the argument that you introduced the way we get in consuming something like the Schrodinger equation applies to the whole universe. It seems to me that something like the Barber-Bertatti model of classical cancers is a counter example, so obviously I've missed something, but maybe we'll explain what it is that I've misunderstood. The Barber-Brittani model is a timeless theory in the sense that it's reprimaturization. All that counts are the curves in the configuration space, not the parametrization of the curve. Yet, if you look at the equation, it's about a T and a T. The Hamiltonian, if you look at the analog formulation, which is the Hamiltonian constraints formulation, they have exactly the same properties of general relativity and they're a very good model for all of these issues so, okay, so

52:30 but you could, but if you look at a different form of action you would say the Lagrangian form of action then there is a T up to reparameterization that's right is it the fact that the Schrodinger equation that makes it immediately obvious to the T. What is it when you can look at the equation, how do you find that? You can try. Now, that theory, so not everybody knows what that theory is, but that's a formulation of classical mechanics. It's enough to say that it has the property that the equations are invariant under changing the time variable to any monotonic function of the time variable. And in such a theory, that says where is the system in the configuration space at time t equals 17 because that's not well defined because you've changed the parameterization so that t equals 17 is anywhere on the curve. So the problem occurs in the Lagrangian formulation as well as the Helicobian formulation. Now, a strategy in that system as in general relativity is to say let's pick a particular of a particular dynamical degree of freedom or a function of them and call that the class and refer the others to the others to it. For example, the volume of the universe gives some definition of what the surfaces of the simultaneity are. if in the Barber recording model there's a particle between particles positioned in space up to all possible translations I don't know, the volume of the smaller sphere, something like that, and the issue is that one can state in terms of such observables, but in the system, one of them is in an all-black integral systems, one can't actually compute them. Nobody can actually invert the equations in motion. This is what is the part of it, actually inverting the equations in motion on the whole space of the initial data, so that you can write down functionally what are the other observables and the functionals of that observable. So there's a practical

55:00 problem that I'm wondering if it isn't really a problem with the principle, A, and B, none in any case people have constructed that way, for models, are actually observable by an observer living inside of the universe. They're observable if you have access to, quote, you know, some external observer. And so the two criticisms apply just as well to the Barber-Bettoni model. I can write a trivial reduction of general relativity, like the Friedman-Ramison-Walker model, where I can invert the observables, and I can do the same for the model. But anything with any interesting physical content, I have those two. At this point in the queue, it's led to the terms of how you are interested in it. We have these principles which I hardly understand, which I don't see enough motivation for most of them. We said that we have a theory and the theory should use only things which are measurable. And we should be able to construct the space we are talking about in finite time using computers and whatever. It seems to me that if I have a theory with a small number of simple equations, many, many degrees of freedom, or whatever, which tell us, and then we add some, whatever, axiom it is, part of the theory, that some objects in this theory correspond to our experience, this is what we can measure, another we cannot, and we, what theory predicts is what we see, even though there are many, many things which we cannot compute, we cannot, really cannot define, there are things which are not defined. So why should be a problem? Because two things. One of them is there's no such thing as a theory with a large number of degrees of freedom and a small number of equations. If you have a large number of degrees of freedom, you have a large number of equations.

57:30 Each of those degrees of freedom of balance, each of those is an equation. We're dealing, we're talking about field theory, where there's supposed to be an infinite number of equations. I think what we do, I mean, let me say what I really think we do. I think what we do is we write down these things like the general theory of relativity, and we enjoy looking at those equations. And we, two really smart people can actually prove some theorems about some solution, about general solutions of those equations. Then, those, you know, some really smart people. What the rest of us do, and we like those theorems and we learn them, but what the rest of us do is we cross that theory out and we replace that with another theory which is guided from that theory by doing things like crossing out all the spatial derivatives, everywhere they occur. And that other theory, we attempt to do cryptology with. And the restriction so made, it is true in some sense that every solution to the theory with the derivative is crossed out, if the spatial derivative is crossed out, is a solution to the original theory. But, of course, that's a set of measure zero of the real solutions of the original theory. Now, one can argue that any interesting physical observable in the real theory is degenerate on the set of measure zero of solutions that we studied. So what we've done, so Friedman, Robertson, Walker is an interesting model of cosmology, and we can measure to some extent its parameters And that's an interesting thing to do. But that tells us nothing about the problem of how to make sense of general relativity as a physical theory, and what the observables of general relativity are, and how we're to measure them. Because it only teaches us about the observables of a theory whose solutions coincide with general relativity on a set of measures zero. And let me, by the way, since you look at this, let me make that argument. Any observable of real general relativity, which is local, has to be of the form. There is somewhere in space-time an event that a certain list of things are true of, which is enough in all, or at least generic solutions, to find that event in that space-time.

1:00:00 So you can, say, write down a list of values of some fields, some local fields, and hope, of course it's never really true, but hope that they parametrize the events in every solution. And then you find such an event, and at that event you look around and measure something else. Every local observable, in the real theory, has to be of that form. And to be well-defined, it has to, with every solution, distinguish every event of every solution. Otherwise, you're not going to be local to this. You're not localizing it sufficiently to make an observation. Unless you can, starting just with the brute mathematics of the theory, all the functions written down. Now, any such observable will not give a proper answer, will degenerate on any solution that has a killing field, that has a symmetry, because there will be an infinite number of events that have the same local observables, known as a symmetry. So, any procedure to construct a local observable in general relativity will fail when applying to any solution which has a symmetry. So, the problem of what are the observables for some set of, for some small set of solutions which have a symmetry, such as the Friedman-Rodson-Walker solution, is distinct from the problem of about what are, or even are there any, local observables and general relativity. Nobody's ever demonstrated even one, a proper local observable and general relativity, as that is, as a function of initial data of the kind that's needed to satisfy these possibilities. And I worry about that. And the reason why I worry about that is because that problem of the classical theory, which you can get away from by saying, we are in a Friedman-Roynstein-Walker solution, or in something that can be described by some field representing small fluctuations on a Friedman-Roynstein-Walker solution. So it doesn't prevent us from doing cosmology, real cosmology, like, you know, guys doing astrophysics, But it prevents us from making an ominous quantum theory.

1:02:30 It also prevents us from making an ominous statistical mechanics of the real theory of general relativity. I wanted to come back to the question that Michael opened with. I'd like to push the claim that you can have a meaningful physical theory, although the computational resources, or trying to work out in detail what it tells you about the world is going to require more computational resources than you particularly allow, or that you want to allow because you can place some restrictions on the computational resources allowed. I mean, Rolf Landau was one of the people who used to bang on about this a lot in his, you know, demand for self-consistent physics. He was saying that there's a certain, Rolf Landau, he's one of these guys who did a lot of work on the thermodynamics of computation and so he was worried about the sort of energy costs of computation and just the general the fact that the physical resources are required to do computations is a component we have to take into account when we're formulating our physical theory. And he was worried by the fact that we can never invoke continuum limits and so on, because that would take an infinite number of computational steps, which is a non-physical computational process. So I guess you'd be sympathetic to that point of view, but I want to come back and say that that you can have a meaningful physical theory despite the fact that you can't calculate what the particular values are to an infinite number of decimal places because there's a distinction between understanding what it means for the equation to be true and actually doing the calculation and there's a danger here of slipping into the mistake of confusing human cognition with machine computation Well, so, first of all, the issue is not just one of accumulating more decimal points. No, sure. And it's not one where human computation and reasoning could get you further than a computer gets you. We're talking about generic dynamical systems which are not intrusible, which presumably, you know, presumably, I mean, there are, you know, presumably general relativity is,

1:05:00 I mean, the three-body problem in atomic mechanics, which is a limit of general relativity, is chaotic. There's another one that can actually give. So it's hard to imagine that the problem of three black holes in general relativity is not chaotic. If it is, then there's some deep symmetry of the equations that could be beautiful to unravel. Let me stress again, the issue is not that we know 50 local observables in general relativity, and whether we know infinite number, but nothing in checking the theory experimentally is hurt because 50 is more and more than we use. I mean, we don't worry about the fact that in quantum electrodynamics, the classical electrodynamics, for that matter, you know, with matter, there may be some of these same issues because we can use the space-time background, because there's no analogous between what they've been doing, to construct a lot of observables, which are good-level observables, and we can check Maxwell's equations, even with matter, as much as we like. The issue is not analogous in general relativity. I'm really claiming that all the observables that we speak of when we say that we're checking general relativity are observables of reductions of the theory to a finite number of degrees of freedom, and are unlikely, not even maybe, but are unlikely to correspond to observables of the real theory, in the sense of locals that I've given here. And you might say, what's wrong with considering the general relativity sits there and we reduce it and then we check it. I would say that's fine for classical theory because classical theory allows you to do the funny thing of restricting yourself to one solution and then asking what a trajectory could find to see inside it. So if you're willing to restrict yourself to a symmetric solution plus some fields on it which may represent small perturbations, galaxies growing, etc. You can do real-time work. And when it comes time to talk about either the statistical mechanics of the theory or the quantum theory, you're not allowed to define your measurement theory or your theory of what's observable inside of one solution. You have to

1:07:30 define your theory of what's observable on a whole spatial solution because you're either averaging or you're performing some quantum habitability, and therefore it's relevant that you'd better be able to describe either classically or quantum mechanically measures on a whole space of the research. And then there are serious technical worries about whether you can do that or whether you know enough to do that. And the appeal to computation is just to try to find clean elements like that. Okay, so it's David Wallace, and then Ken U, and then Harper Field, and then Simon, then Harper. Okay, that follows on by Chris, actually, because I want to ask about this, um, computer, this is obsessed with the afternoon, that's the victim I like. Now, I can sort of see the motivation, it's going to be something like, I want to, I want to actually do the calculation, if I can't do it in a computer that fits my life, and then I can't do it. But it seems to me, if we had a theory, it could be done by computers in the saturn part of the night, but it was the science of the Virgo's Libra class to be running for five billion years, that would quite hold comfort. So it seems that that margin is almost, if you want to margin there, it needs to be something like, it could be done with the realistically available resources of actual beings who devolved in the actual universe, or could evolve in the actual universe. and this has now become an incredibly strong restriction. So when there's some formal justification of this inside the Park Light Cape that... Well, by Moore's Law, just, you know, the capability is increasing exponentially. So what's computable by the Virgo supercluster now, essentially, will be computable on my wristwatch. So, I mean, this is, I don't, you know, the point that I'm making is, I mean, you can train this anyway, But the point that I'm making is that we have no idea how to construct any observables in the real full dynamical theory that we're putting in the region to correspond to a pre-local observable. Yeah, that seems funny. I believe that's not what I'm just concerned with. There may be a better one to say. My question is very simple, I think you can ask it within one minute.

1:10:00 Okay. I don't know whether I understand you correctly. I think that you are asking about the observer and time. You try to ask for the privacy of the notion of time. And again, you mentioned from time to time, three different contexts, cosmology, cosmology and cosmology in general. Do you think that these three contexts would be equally suitable for the understanding of the kind? That's why you even think about it. And you're asking for the privacy of notion of time is essentially based on the idea of observability. And can I explain that actually your philosophical case is a kind of an argument for the necessity of time. I just want to ask you, you just can't hold it. The second thing, I don't know enough, and the first one, I think your argument is equally interesting in those three contexts, but it is different technically, so I've tried to mention these two in a second. Sometimes you emode this kind of context of cosmology, but there's a strong arching that the specific of cosmology is not necessarily to use the context of cosmology. Oh, okay, so let me address that. First of all, in class, there are three kinds of systems we can study. Systems which are spatially compact, systems which are spatially compact with boundaries where the spatial slices have finite boundaries. So the boundless systems are spatially finite, but they're boundaries. and systems which are, which have boundaries but are infinite, such as the asymptotically flat or asymptotically anti-distributed. One can try to do quantum gravity in all three contexts. What do you want to do with quantum gravity? We don't really want to do any cosmological

1:12:30 We just, just focusing on the best, more we'd like to tackle, and then we study the business. Yes, and what, so first of all, A, when you try to separate out the issues that have to do with the lack, it's not an issue of complicated, it's an issue of can you, and it's an open issue, formulate a quantum theory of gravity in a system with boundary, either finite or infinite. in such a way that on the boundary, because of the way you fix the freedom to make hippomorphism, on the boundary there's a conventional notion of time external to the system, and you have a conventional Hamiltonian formulation where there is a state that depends on the external time on the boundary. and people work on that and it's interesting and some interesting results have come out of that the most interesting results that have come out of that have to do with the relationship between the area of the boundary and the amount of information that can be measured on the boundary the result is that the amount of information that can be measured on the boundary or consistency with the laws of thermodynamics must be less than 1 to 4, the area of the boundaries and consequences. And that's a very profound indication. It's a recollection of results and arguments. And it's not a proof, but an indication from several different approaches to quantum gravity, including string theory, quantum gravity, black hole thermodynamics. And that in itself, that result in itself, throws a whole different mind on these issues, but that's another problem. Yes, but that's a good moment. It is not so sensible to some stepping of it. You see, we have to act on one hand at the time, but at the same time, not at the same time, at the same time, before and after, he goes to the philosophical position of time, relation is the view of space and time. No, I think that the fact that the theory has formally the gauge invariance that says that, and let me just speak about time, that however you parametrize the solutions,

1:15:00 that they're completely labeled arbitrarily the time parameter on the trajectories. There are arguments that say so. It means that any notion of time has to be relational. Meaning there are no observables of the form of what's the value of something when the time parameter equals 17. There are only observables of the form of find an event on a trajectory certain degrees of freedom means 17 and ask what are the values of other degrees of freedom. So I think that it's practically an implication that reparameterization variance means that we're dealing with the system where time is relational. And I'm assuming that is part of the balance of what I'm saying. Yes, but for a time in open time based on causality, based on causal factors. my way out, is that a notion of time, or that captures some, not everything, that role that time plays, which is sufficient for our purposes, is causal structure. And my conjecture coming out of the discussion is that causal structure should play a role in the quantum description of the history as fundamental and as a classical description. It's very fundamental, but I'm not as fundamental as the adaptation formulated in a low shot for relational. Well, so the positive suggestion is that it's not enough just to say the time is relational, we want to know what is the nature of the relationships. Given the different relational theories, all relationships of the question will be different. the nature of the relationships in the kind of theory pointed to weakly, in other words, seemingly weakly, by these considerations is that they're causal relationships. Thank you. Harvey Fields, then Simon, then over. I just wanted to confirm two things, which I think follow from your presentation, but I'm not sure.

1:17:30 The first is that the outcomes of present-day cosmological measurements are legitimate constraints, they're often legitimate constraints on the formation of cosmological theory. Is that correct? We hope that that's true. I thought that sort of follows from what you've been saying. Why don't you regard it as legitimate constraints? Well, no, I mean, I'm confused a little bit with the logic of how you put it. It is to be hoped for, and there is reason to believe it may actually be, that there will be observations made by us by using satellites and things like that, which will constrain the quantum theory of gravity. And such observations are under discussion as we speak. Well, they're obviously made by us within the universe. Okay. The other one is, you seem to be saying that we are sort of driven to the idea that causal structure ought to be regarded as central in some theory. So presumably, does that draw out any, what used to be called, block universe models? Yes, what used to be called the Black Universe model, I'm claiming that the Black Universe model was something that was only realizable in models or by waving your hands in the air. Okay. Sorry. I want to wave my hand in the rest of it. Can you come back to Fatini's? Sure. One of the two. I think that there's been a tradition in philosophy about virtual reduction and whether our civilization is given too late can be allowed to die and so on to future sex offenders. And right or wrong is a deflection review of this which says that look, we're not going to have a crystal ball, we're not going to have any guarantees. That surely isn't what the problem of production is about. And I think in this context, it's surely right, that we just aren't ever going to have any guarantees

1:20:00 that some big options are going to come into that setup and very much change the things. So we're not going to have any guarantees. You're sure we're not looking for any guarantees. I'd like to ask that very often. You're not looking for it anyway. So now what I'd like to say is that there must be something right about assuming that how past that term is somewhat technical. But at some level, we have to operate on that strategy. Indeed, it used to be dignifying the brain of cosmological principles and so on. Now, surely there's a difference between saying that and going all the way to the idealisation and you said no, let's do more than that, let's tend to real homogeneity, but why can't I don't think we'd be doing that, but just exporting the homogeneity that we've seen elsewhere. Why isn't that something in between? It's not information we actually can show, but it seems a reasonable strategy, given that we have that principle, I have an answer. Of course, what you're saying is quite reasonable and there's nothing wrong with doing that in classical cosmology and that's what people do. When people make numerical studies, they take a piece of it which ultimately did not figure that our past life only involved in America, and that's compared with the distribution of counts. I'm interested in this argument because of where it leads for the purposes of distracting a quantum theory. And again, I'm here, I'm just borrowing the unit for Tina's work. So, where it leads is the notion that there is no observables algebra, which is, quote, the observables algebra of the universe.

1:22:30 There is an observables algebra for each of these past sets. Therefore, a quantization, in which the observables algebra is turned to an operator algebra on a Hilbert space, cannot be made in such a way that as conventionally there's one Hilbert space. Instead, there may be a Hilbert space for each pass set, which has its own observables algebra, and a map of some kind that allows you to deduce from the density matrix in one some information about the density matrix in another, incomplete. And that's along the lines of, I'm not saying all the steps, but it's along the lines of her proposal for quantum theory of cosmology. Now, in such a quantum theory of cosmology, from then on, all the technical details are different. Especially if you combine that with what I was moving into about the holographic principle, who said that if any of these if we actually think that actually these are not points these events but little finite regions the little finite surfaces on which information comes in then each of those silver spaces is actually finite dimensional and then you have a completely different kind of quantum technology that people were trying to construct when they imagined that there was such a thing as the observable algebra of the whole universe It seems that there's two things going on in this book. One of them is alternatives to . And these are all exciting . But as this was also noted as an argument against monogravity, now what I would suggest is a cosmological principle which isn't supposing humans as a genius, but it's simply supposing that the sorts of monogravity that would work for the monogravity approach. object to this, and objection, this is just now an alternative point forward. Remember how it seems to be an objection. Um, yeah, perhaps, although the, I mean, the thing is in so much trouble that I don't think

1:25:00 something like that is going to help it, and technically, I mean the problem, there doesn't There doesn't seem to be anything interesting from the point of view of the issue of constructing the observables that I mentioned, which is slightly more interesting than spatially homogeneous. But still, not just a linearization around, but still retaining the whole dynamic of content. So I don't know how classically to get at your middle ground, but I don't know how to But somebody might question you. Right. Well, I've got some concerns about what you said, private stuff, and also what you were saying about relationships about time. One thing, I want to hear on the point, say, I mean, there seems to be a bit of an equivocation between what time was and what reason the cops were. And you were saying that, you wrote down the show information that said this T is a reason on the cop. Well, it's not clear that one has to be that operationist about it. So that was wonderful. The other was, when you say that, you know, this re-parameterization of variance or the diffimorphism, the fact that we're using this notion of relative configuration space means that all that's important is coincidences between say a clock room 17 and something else happening i mean presumably you don't want it to be an hri fact about your cosmological theory that you need more than one field i mean surely you have a well defined i mean surely these um models which only have the metric represents you know this idea that was around 30 40 years ago that everything might be space time yeah I mean relationships seems to me that you know the idea that team

1:27:30 but you can still have relations between bits of the universe, you don't have to understand that in terms of the various things at one scene. So, two things. These are my inputs, and I do take... There are several things, spatial, the spatial part being relative, integration space, and reprogrammatics. So let me first do the reprogrammatization. I just take it as input that any physics, that general relativity has that property, and any theory which is going to reduce to general relativity appropriately will have that property. And I take the binary pulsar observations as a strong argument that the parts of general relativity that are the space-time geometry is dynamical, that make use of that, as well as the counting of the degrees of freedom that you get from that. If you didn't believe this and you tried to do the calculation of the binary pulsar, you would believe that there were three degrees of freedom radiating rather than two, and you would get the wrong answer, as people did at some point. And similarly for that, so I take these as lessons we've learned from general relativity, which are likely irreversible. If somebody comes along and tells me that really the right theory of quantum gravity has a fixed background structure of space with a fixed metric and a fixed time parameter, which I hope we haven't so far observed, and somebody comes and tells me, tough luck, that's the theory of nature, then I'm going to design the right novels. than nothing that the community of people that I've worked in my whole life couldn't look like that. These are things that, these are the lessons that we draw from the physical theories that we believe in, in the limits that we believe in. I'm going to, you can be in the queue again, I don't know, but you've got a queue, you see, so that's alright, I don't know. Are there any, let me make a small intervention here. Are there any, I mean, because you're going around with the same theory, but what not, so thank you, that's a good point. I have, I've been looking without seeing hands, but is there anyone who hasn't yet? No, okay. So, in fact, there is Lev, and then David,

1:30:00 and then Harvey Brown, and then Simon, and then Fuchsia Scott. So, and then... May I still want a small clarification? Can you put your two principles? It's not trivial for me that people are fulfilled by, let's say, automatic dynamics in a flat space. I understand that you presume that there's no problem otherwise you can actually because you have all problems of self-reference and people want to ask kind of two detailed questions that two probably will not be correct. So you probably have to kind of... or you believe that there are no problems whatsoever with this kind of theory. No, and as I said when I took the market, maybe the... and I would be happy for any way to weaken these who still leaves me feeling genuinely... Okay? We are working with field theories, passively and fundamentally. Either the fundamental class of field theory is that there are an infinite number of theories of freedom in the physical system and in any finite binary universe. Either that's true or that's false. If it's false, then we should not be using anything other than, if it's false then there are actually a finite number of theories in freedom. I don't know, I'm not too much aware of it. I still believe that most of these are related are only finite numbers. Well, I... Alright. It's just very big. But finite. And if it's finite, that all this is not relevant? No, of course it's not. It's still relevant because, as you said, it's very large. So, okay, so let's take that crunch. I was going off what we were going on in the last second, but I'm happy to say finite is very large. In fact, I'm happy to use the Fettenstein Bound to say how large. The number of degrees of freedom in any system is proportional. Of course, this gets us in loads of trouble, but it's proportional to the area in Ponte. I'm happy to tell you. That seems there's argument that that's true. Now, having said that, I agree with you. There's still problems of principle for field theory.

1:32:30 There's ordinary Ponte field theory. That is, there are going to be lots of things that we can't measure in ordinary quantum field theory and lots of things that we can't compute. But we can compute some things and compare them with some observations. So, maybe I'm just agreeing with your criticism and I can weaken this to... There should be some quantities that we can compute and which we can observe. Thank you. As I understand it, in GR, there's more weirdness than just the parametrization variance. We've also got, I guess you could say, you've got space-specific variance, you've got not just parametrization based on trajectory, you've got a sort of sheet, you've got a space to describe the same solution. Okay, so, and then the canonical program often sort of skates over what we're going to do with that. So the question is, firstly, is anything important that you say was affected by or sort of change by allowing for that command? Secondly, is that sort of space-time command something you'd expect to survive in the sort of things you were talking about towards the end of the talk? So the answer is yes and yes. And in theories based on, in classes of theories where causal structure is predominant, is part of the description of the history, then there is still a reduced notion of what you call Lorentz covariance. That is, if I give you a causal structure, that is, a list of events with their causal relations, and I think I can say this without drawing a picture, then there is always the analog of space-like slices, that is, there are events that have no causal relations amongst them, And which are maximal in the sense that you can't add any other of that. And those, if I remember rightly called impact chains. And there are some causal sets, there are some causal structures, which are sliceable in such things. And many of them are sliceable non-equal.

1:35:00 When that property, when it exists, it depends on the particular cause of drugs, but when it exists, corresponds to what you were calling the local emergency, the fact that you don't have that in your time. I'm just thinking of the special case of the question, if you define a curve, and suppose What is it that you're looking about to have? Some physics that actually gives you a geodesic, I mean in the form of a geodesic principle. All you need is a directional point of configuration. You need to. Now, a separate, you could say in a sense this is a timeless theory because you just have rough configuration space and a curve. Yet, there will be situations, there are theories in which, even though you formulate a theory that way back from the beginning, there were a little privileged parameter on the hill, and Barclay decided there was a basic point. It's a privilege parameter. It's a privilege parameter. In Barclay, we're totally stupid. Yes, exactly. Yes, I agree. There's a parameter enormously simplifies. Now, that's the fundamental difference between this fragment of the Italian accounting that was being occupied in general. And this is really the point that I understand made by the correction. The issue is not generally covariance. The issue is not whether I can substitute parameters or no. Right. The issue is whether or not the equations become simplified. Fundamental equations can simplify the actual . Right. Now where does that distinction come into all of this discussion? Thank you. I neglected it quickly. Certainly, so just the background for other people, that's a possible solution to the problem of science in cosmology, which is called deparameterization. Supposing that you could find some function of the dynamical variables which played a role precisely as time. And what it means, the standard way to say it, is that the hematronic constraint that's supposed to be for zero

1:37:30 would turn out to be of the form of the momentum conjugate to some zero variable plus some function of the other variables, where those are the coordinates and those are the momentum, okay? And then this p, then quimechanically, this p would be like d by d x0, okay? Plus h of the p's, or the other p's in the q's, okay? And all of this on a state would be zero when we can interpret it as a way with a shorting equation. And that's a proposal which several people's careers have very valiantly been devoted to trying to realize, and nobody has realized it so far, although certainly Julian Barber and colleagues have a new claim, which is, if I understand right, the possible existence of such a thing in a theory closely related to generality, not quite generosity, but possibly closely related to generosity. And I don't know that's a value like that. If such a thing could be found, if such a particular choice of a variable could be found, then it would be very interesting to try to make a quantum theory of gravity that way. One would be home free because one could worry that that time variable, here, the x0 variable, one should still worry whether that's actually observable by local observers. But one would certainly be, one could go down that road quite a bit and ought to if there was such a proposal. And what has prevented people from going down this road, and why I didn't mention it, is that to this day, no proposal like that succeeded where, let me just hammer, what I mean by succeed, you can always, you can choose any formally, but this function should be a nice enough function of the p's and q's that when you go to the quantum mechanics, and these are operators, that you can actually have a procedure to construct this operator. And nobody succeeded so far in doing that. If somebody could, the game would be changed, I agree.

1:40:00 Well, now, I'm not going to cede a little chairman of the comment here, because I thought you, what you said before about I would resign and write novels, was you would resign and write novels if somebody found such an X-naught in GR, right? But now you're quite sympathetic to Barber finding it in conformal casa. I didn't quite mean this. I meant, I didn't mean that this x here was a function of the normal curve, but I meant if it turned out that really there was just some fixed baseline background, and therefore kind of like the focus of this kind. Oh, I see. Okay. So there's a difference between what would make you resign and this? Yes. This might make me just have the right philosophy. I'm not sure I can see it. Not for you guys, not for me. What would make you write comic books? Well, can we, we'll stop a minute and let our overworked speaker off, if you're having a break, but Simon, you have in the queue. Well, can I, just a brief comment, just a quick comment. One of the models, this is one of your major, And it seems to me you've got pretty major... Oh, thanks, because I forgot to come back to that. Thanks very much. It does seem to me that the literature knowledge, of course, then you're very familiar with it, but I think you immediately jump to quantum mechanics and sets them down both in the classroom and in the classroom. The quantum theory, it's got to be interpretation depending whether or not we have a similar problem. In the pilot wave case, it has a few years, but in every other, rather logistic, what we can't come into interpretation, we can't use theories, in every other case, we don't. Not even state deduction, we don't have a lot of evidence. So, why do you say, well, in the air-racking case, we have four possibilities. And of course, there's an algorithm to take you from 10 years after Big Bang to one branch 15 billion years later. There's no such algorithm. So, I'm very proud to keep on all this in the same direction here. That's a good question. Let me make my worry about novelty. novelty, let me make it into this original context, which is biology or economics, because

1:42:30 of course, if physics is a theory of everything, if physics is a theory of physics, of course. Could we imagine that there is a finite procedure that would allow us to write down the 100 the 100 most populated job categories in 100 years, and for the 100 most populous species of mammals in 100 million years. So if there is not, then there is an issue of novelty at that level and therefore I think there is an issue in physics. Yes indeed, but I'm not just saying that, I mean I have to say it's actually not accurate. Indeed there is no such algorithm. I think there's a problem with novelty, because there is such an algorithm. So I think someone's saying, yeah. So now my question is, having agreed about that, If the structures that we're supposed to work with in making a classical or a quantum theory of gravity, by virtue of the special properties of gravitational theory, particularly the morphism invariants, land us in the same issues, and now we're not talking about biological species or pit records or something like that. possible geometries that could be measured on the small and quantum gravities, there needs to be perhaps some worry about the standard idea of how we do dynamics, which is we write down a priori the space of all possible configurations, a priori, and then we look for an equation that determines the trajectory. And if there's not a finite procedure to write down the space of possible, of all possible configurations,

1:45:00 then we don't get to run the argument of write down that space, find an equation to write a trajectory on it, and then go through this problem that the observable functions on the other trajectory. I think we're going to decide cospefaces because of course I agree with everyone saying that it's a classical gene. If you're talking about quantum gene, then... We're talking about quantum gene. Well, yeah. In terms of quantum gene, we have to say something about quantum gene. And if we're going to address the issue of what is observable. No, so let me say something about the quantum measurement. If it's true that the quantum states of geometry are given by embeddings of certain kinds of graphs in a spatial manifold up to 15 more things, then it may be that there are observations that I can make, that it's something that I can measure in a finite region, where I don't know, So, say a filter, in conventional quantum physics we make a filter, we pass a reason through it and we see things come out or don't come out. And it may be impossible in principle, for certain observations, to make a filter that we know returns one orthonormal phase of space. But to say it another way, we may not know the dimensionality of the subspace which is picked up by the filter. And if that's true, and the indications are that it may be true, then we have a problem with the standard notion of quantum measurement. We have a problem computing probabilities, we have a problem doing quantum channels. I think it's not just the issue, it's not just the term. The issue is, and maybe, and I think that this is something more interesting than just the standard discussions of emergence.

1:47:30 Because the standard discussion of emergence is, how do we relate some high-level property to some low-level property? The issue is that there may be high-level properties about which laws can be observed, and in some appropriate language, deduced, which may be reducible, that may be fine, but which may not be predictable given the low-level properties. That is, one may not be able to predict the language needed for the high-level properties. And it's that inverse thing, which is harder and which really doesn't mean if you... I'm bringing it down to space-time, where I think it's a worry, but in its original form, it is a possible argument against the existence of, say, a theoretical, you know, a theoretical evolutionary theory. Could there be an evolutionary theory that is predictive, or could there be an economics which is generally predictive, and this is a possible argument against such a thing. It doesn't mean that evolutionary theory is not science, but it may mean that there are things that one could never get out of evolutionary theory in a way of predictiveness, and that would be good to know about. we will stop your friends time is short Lee thank you so much for coming for spending a discussion