Dynamic Agents & Geometrisation / Geometrisation(s) of Matter (contd.)

0:00 to know the human being, the human being. And the job that I've done in all three of the first words of Christianity, I have the same imposition I live, to be far back, and the concept to think about the human being, is a tool and more work, but with respect to the parisianism, Ishtani and Magdalena start this session. Ishtani and Zanaka are the same thing that when A as to our word of A and B, if there are some of the two words going here, then I can say that everywhere, in any time, it was the word of God. Magdalena says, if The world has created the world being, and it will be coincided in the world peace. It doesn't mean that the world peace is coincided in the world peace. Because our sense of the form for our clients is diverse. and it is very important to talk about what I have is continuity, which is a continuous function continuity which is distance, which is a measure in general, what is it here? in the kind of theory, you need functions, continuous functions as a paraphernalist, what can I say, can we have a sensation? It seems to me they go to A forward B, and then forward B forward C, but now, which one? There was one, but that's right. This is the surface. Look at A, B, B, and F, and the front from C. And so, we can run this information. It's our mind which constructs the notion of belief that we need to deny the President's function. We look up. First time, just ask this question. Well, I think there's no time for any other questions. I don't know if people have.

2:30 So, thank you again. Thank you. I have to restart, please. Okay. Okay, so the final speaker of this session is Adan Seuss from the Autonomous University of Barcelona, whose title hasn't changed absolute objects and general relativity, dynamical considerations. Thank you. General relativity has put to be a rather elusive notion, and after Gretzmann's objection, we know that a nearly formal understanding of general, sorry, general covariance, I wanted to say a little bit more, so I don't know if I said general relativity. A formal understanding of general covariance is not enough to distinguish general relativity from other space-time theories which incorporate something like a fixed space-time structure. The best thing is just push the arrow down button.

5:00 So, which one? Well, Dennis takes the keyboard. Oh, okay, yeah, okay, thank you. So, I would say that a formal understanding of general provenance be enough to distinguish between general relativity and other space-time theories with space-time structures so the challenge is to try to find a notion which is related to general covariance but which can very fast to distinguish between these two types of theories and James Anderson, in the 60s, started a program to try to do so by introducing the notion of offshore literature. This was taken up by Michael Friedman, who did some reformulation of the program. And in this talk, what I want to discuss is where this program is suitable to explicate something like a notion of background-dependence. Here, when I say background-dependence, I'm going to refer to this feature of general relativity that distinguishes from theories with fixed space-time structure, but obviously this is And I would try to defend that, I would argue that the program, as usually is understood, needs something like a slight modification, because usually when one reaches absolute objects, one defines background independence in terms of the lack of absolute objects, And I'm going to pretend that the program is better understood as a substantive, providing a way of making substantive statements about the symmetries associated with different disciplines. And I will do this in the context of the discussion of the last or the most recent counter example to this approach. So first, I want to briefly get what the Anderson treatment program is, and just to start, I'm going to take, and I think this is Anderson's intuition, the guiding metaphor, the guiding intuition behind this way of trying to understand background independence,

7:30 is to say that a theory is background-independent if it has no objects which act and are not active at all. So this is the idea that we are going to try to be more specific content. And there are three main elements in the program. One is the definition of the array, which which can be stated by saying that the covariance group is the symmetric group of the equations of motion of the theory or in terms of model, if you have a solution of the theory where M is the space and manifold and O is some geometrical objects on the manifold and the field equation is going to give you the relation between these geometrical objects So the covariance loop changes from solutions of the theory to solutions of the theory by applying these transformations to every geometrical object. An absolute object then can be defined by saying that it's an object, a geometrical object, that is the same in every solution of the theory up to local transformations of the covariance loop. So in this sense, these are structures which are fixed in the theory, and then Andersen defines the invariance group as the group of transformations of the oscillators, or the transformations that lead the oscillators. With this element, we can try to define background independence in two different ways, and one is saying that a background independent theory is one that doesn't have any absolute subject. Another way is saying that, making a statement about the invariance group, and we can say that a black-grade independent theory is one for which the invariance group is the group of all possible coordinate transformations of the diplomatism group.

10:00 and usually these two ways of in the Anderson Prima program these two ways of defining background independence are equivalent and in the discussions about the program and when people have tried to find problems of contact examples to the program What they've taken is that the program is telling you that about grand-independent theory is one that doesn't have absolute perception. And why one can do that in the language of my program is, well, because if one takes, we can take the covariance group to be the whole distribution group, because, let me say, it can be formulated in a generative covariance form. So, if no objects which are the chemotician invariant are admitted, or one makes a special category for them, then these two ways of defining vector-independence are equivalent. So when views on any absolute object, the covariance group is equal to the influence group, and the reverse is also true. So I want to stress that, I mean, it's not quite obvious, but this equivalence, this equivalence between background independence and lack of absolute objects is ensured by this fact about the kind of objects we think they are candidates for absolute. So we wouldn't say that a constant scalar is an absolute object. And also by the definition, by Anderson's definition of influence. This conceptual scheme has been discussed for quite a long time and several counter examples have been found and here I want to concentrate to one which finds an absolute subject in general volatility with no sources and this is what I need to discuss.

12:30 So, I mean, this way of trying to explain background independence has problems, and it has one which is quite tragic for the purposes, initial purposes of the program, which would say that general relativity is not a background independent theory. And, well, one can also criticize the program from a conceptual perspective, more than Frank and Ty, for example, and Gordon Bellock gives some ideas why he thinks that the international film program is not going to succeed to educate them of an impact on independence. But maybe I'm going to move to that. I'm going to move to discuss the counter-example that I have mentioned. It was proposed by and it can be presented in the following way. There is a theorem from differential geometry that tells you that for any metric whatsoever, and in particular for the solutions of Einstein-Field equations, there is a local coordinate system in the neighborhood of any point for which this quantity is square root of minus C is equal to 1. So, this is a scalar density, made up from the determinant of the metric, and according to a local definition of absolute object, this is going to be an absolute object. The standard use of the Anderson Friedman program says about general relativity that this is not an ultra-independent theory. And if one computes what the invariant group for this theory is, instead of being the whole of the human-fishing group, it should be the symmetry group that has checked.

15:00 And this is the volume preserved in the human-fishing group. So, just to repeat myself a little bit, this is a counter-example of the identification of background dependence with the lack of absolute subjects, but maybe it's used with the case that it's a counter-example when one uses Friedman's definition of absolute which is local, Anderson uses a global definition of absolute objects, and includes objects other than sensors and connections in the interior geometrical objects. So, strictly speaking, for Friedman, this would not be a counter-example because he is thinking only of geometrical objects that have sensors and connections. And the same can be said for Anderson because he uses a global definition of obsolescence. But if one thinks that in order to, I mean some examples where one wants to apply the Anderson treatment program, you are going to have objects which are not sensors like this one but there are other examples. that it's good to have a local definition of absolute subjects, then this is a problem for the correct order. So I think it is useful to compare what happens in general volatility with in modular volatility. And this is a theory where the starting point is dividing the metric, decomposing the metric in this way, and taking the scalar density as a fixed quantity given a priori and writing a theory where the only variable is the metric density g0. So one can do, can write a general equivalence action for this, from a general equivalence. And from this one can derive the field equations and these are basically answer field equations with a cosmological term, and a condition on the value of the coordinate conditions.

17:30 So if one uses Anderson-Friedman's program to see what it has to say about unimodular relativity so obviously it says that this theory has an absolute subject and it does using both Anderson's and Friedman's definition of absoluteness and the one can argue that unimodular relativity is equivalent to general relativity with cosmological constant, plus a global coordinate condition. But it is not equivalent to general relativity without the cosmological constant. It is one way to get, in order to get a general by drawing action, one introduces an arrangement with the flyer and then this plays the role of a cosmological constant and this is, so this lambda seems necessary to introduce the constraints of, on the, on this quantity. So the question is, using Anderson Friedman's program, do we have the same invariant view for the three theories, and here I mean the general relativity with no cosmological constant, and general relativity with technological constant. So, what the standard use of the Enso-Stream-Bach Program says is that we cannot distinguish between these three theories because they have the same inferences. And this is a consequence of having a definition of invariant truth that depends only on the symmetries of the absolute process. But we can observe that in general relativity without cosmological constant, there are some

20:00 degrees of freedom that we are not taking into account. And this is because the theory is a scaling program. So, even if we can fix, I mean we have this absolute subject which fixes the value of the scalar density in a neighborhood, and this fixes the volume element up to a constant, the theory is a scalar imperium, so we have this extra degree of freedom in the value of the volume element. So, intuitively, this extra degree of freedom should be taken into account when computing the impedance group and they should enlarge the impedance group and we should say that the now the impedance group is not the volume that's in the tumor but this group products the different values that this volume element can take and this is So, by making this contrast between general relativity and minimodular relativity, what I want to first stress is that what I call the standard use of the Anderson-Kidman program gives you an anti-intuitive result by saying that the inference group of in modular relativity and general relativity with a cosmological constant have the same inference group. So this might be a reason to try to question what the logic of the standard use of the Anderson Frequent Program. But, I mean, relatively to this one, I think there might be other reasons, we can formulate this reason in a different way, and we can think that it is strange that the definition of the invariance truth depends only on the formal features of the absolute subject. So we can, maybe it's useful if you try to think of two different theories, where in both of them we have the same absolute subject, but they enter into the theory in a different way.

22:30 The Anderson Friedman program would say that the invariance group for the two spheres is the same, and maybe what one says about the invariance group or the symmetry group of the theory should be more dependent on the dynamics, or the way the absolute object relates to the other objects. And this doesn't seem to be captured by the definition of invariance in some cases. And another concern is whether the use of a local definition of taxable subjects may be a global decrease of freedom that one wants to count as belonging to invariance. So, I think the assumed equivalence between background independence and lack of absolute process is not necessarily true, and one could try to use alternative definitions of invariance which is to modify the original Anderson's definition and here I propose one is to take to the finding parents group as the subgroup of the digital artisan group such that for all the transformations you belong into this group it takes you from solutions into solutions applying the transformations only to the absolute objects and living in other objects and chains. And here I also propose that maybe this definition of invariant has the extra advantage of providing a way of explaining what I said here, the acting part of the metaphor I was talking about at the beginning of the talk,

25:00 by trying to relate the invariance group to the degree of acting of the absolute object. So, in order to define the invariance group, it's not only important whether the theory has or doesn't have absolute object. Also, whether to what extent these objects act on the others, on the other geometrical activity. So, I think a definition, this type could capture this idea because the bigger the invariance group is, the more transformations that change the absolute objects, without changing the other objects, so we could say this means the less the absolute objects are. So, just to conclude, to summarize, I argue that the definition of local absolute objects leaves space for the views of freedom that might be relevant for the influence group, a definition of invariance group that includes these degrees of freedom could break the equivalence between background independence and lack of absolute subjects implicit in the standard use and a definition of background independence in terms of invariance group is free or might be free of most of the problems such as in the Korean American Freedom Program. Thank you. Okay, I just want to go back to the counterexample. You said that we can do this as squaring from minus g equals 1. We can do this without any metric. We can define a local coordinate system. Is that right? By defining the coordinate system, we can arrive at this. The square of the planet has a fixed value in there. And you said this, in some way, reduces the symmetry group, or the invariant group. But compared to what? I mean, the only thing we've done here is to reduce a local coordinate system.

27:30 So, what exactly, I mean, when you say reduces it, what is it reducing it compared to? And I wonder if... Right, so maybe I didn't express myself clearly, but what I mean is that if one assumes that the invariant group for general relativity should be the whole dichematism group, and you find out that this is an absolute subject, then using Anderson's definition, the invariant group is the symmetry group of this subject, so this is going to be reduced in the sense that it's a smaller group of the whole dichematism. Okay, but still it's only an absolute object within that local coordinate system that we've justified. So rather than saying that it's introducing and somehow there is an absolute object there, we've defined a local coordinate system which allows us to see the metric, or which sees the metric, that local system sees it as it has some kind of absolute object promoted to it. I mean, this is, yes, this is Friedman's definition of absolute subject, I mean it's local, it's defined, the equivalent between the subject in two objects in order to be declared as absolute. You should match one to the other in the neighborhood of any point. So it's a local, a globally local definition, or locally global, I don't know. Can you speak to the slide that was your proposal about the new definition of the So, what is A.J. or G.R. without a cosmological constant, so it stands back in G.R., A.J. is this G.R.

30:00 Yes, I suppose to do this properly, one should take a formulation of another identity where both the metric density and the scale density are variable, and you can write an attention for them. So, AHA would be the scale density. So, is this really going to be true for a full difumorphism group? Because you want the invariant group in that case to be a full difumorphism group? I think it is, I mean, I'm taking that this is true, but I think this is true to you. So you are trying to imagine whether for some lithium systems the definition is not true. I think, well, I think that the definition includes scale transformations, but one and the other would not. I mean, if you're leaving the matter fields as they are, changing the... The muscle thing. Well, I'm taking that. Thank you, Gio. My question is also to the affirmative. I just wondered, is it an necessary condition for the group to be the embarrassed group? of the absolute object, but it would be a subgroup of the different organism group. Because if you have an extra symmetry, if you have a theory with an extra symmetry in addition to a different morphism group, say you have an additional SU2 symmetry, then you could say, I can't have an absolute object with respect to this new symmetry group,

32:30 maybe exactly by this definition, but it doesn't have to be an absolute object with respect to a group that is a subgroup of the different organism group. Does that also work? Or why not? I don't understand completely the question. So you're wondering what happens when you don't... When you don't demand that you're going through the susceptible work that you don't want to do, whether the definitions will still stand and do what it's supposed to be. I don't have an answer, sorry. I have thought about that, but I haven't been able to... Yeah, to find... I mean, usually this is a condition that one includes... OK, well I think we've just got to half past seven, so we should thank all the speakers again. I've looked at some of it, I've looked at some of it, but yeah, I was reading through it, I printed it out when I was reading it, you know you've got to save time. Thank you.

35:00 Again, there's a very interesting talk being given there. Nice to see you. You might have an extra couple of times. I think you're willing to get to look at my temperature and my system. About the . You sent me this abstract on that. There's a lot of time. I'm not sure. I'm sorry. I'm sorry. I'm sorry. I'll have to send the abstract. Oh, of course, I'm going to do that, but I'm actually going to be on the bed. So you can actually watch it. Yeah, yeah, well, it sounded to me like it was very interesting. Thank you.