Dynamic Agents & Geometrisation / Geometrisation(s) of Matter

0:00 I was going to ask you if that would be okay, because I'm going to miss your talk that, because I'm going upstairs for the philosophy of math thing. That's what I thought. I don't know if that was funny. That's what I was going to do with my mind if I would, yeah. That's, you know, I'm sure you'll have lots of new things to say. I was just a little bit jerking with Dennis, because of course I recorded you were talking in Paris in April about the adjuncts. Yeah. I've ever been talking, yeah. So sorry. I think probably, no, I think it's just every has its own glass, but I believe we go out one after the other. So, you know which one's Mark? Oh, yeah, I'm sure. Yeah. Hi, Jay. Are you going to this one? Yeah. He's supposed to be the chair, but his flight came in the afternoon. So, if there's no delay, he will be here. So, who's the chair? Thank you. Thank you.

2:30 Thank you. That's sort of all, that's, yeah, you're looking for all of the things that make it. Yeah, yeah, yeah. Okay. It's good, because I was supposed to chair the session yesterday. I'll be sitting in the back. He's just running a lot. All right. Who's started here? Oh, so he's on the wall. Yeah. You know, like, oh. from Rome, from Rome, yes. I want to speak from a B.G. man. Then give me the test of the month, we can be lots of them. Oh, no, but yeah. That's me. Why not? Well, I'm a black guy, actually. I'm a black guy. I'm confused. Hello. Oh, that's the right thing. You are. That was great. Thank you.

5:00 Thank you. Well, I know you think that the government might have been in Brazil, I have no idea, you know, that's one thing we have, if you're, no, I'm just keeping the storytelling, I'm just being, okay, do you want to say a minute, or is it right, or is it what you read about that story? about thank you thank you Thank you. Thank you.

7:30 Welcome everybody to this session entitled Geometry of Matter. Each talk has half an hour and to perhaps allow people to move between sessions but to make sure we finish promptly at 7.30 I'm going to be quite strict or try to be quite strict with keeping to time. So So, without more ado, let me ask Norman Zeroka from Zurich to give his talk. Thank you very much. So the title of my talk is Dynamic, Agents, and Geometrisation, a Weidel approach towards theories of matter. Around the middle of the 1920s, Hermann Weidel distinguished three different types of theories of matter, namely substance, field and agency or agent theory. In what follows, I shall sketch this distinction and take some of Wiles' own examples as an illustration in particular for what he calls the pure field theory and an agent theory. Then I shall briefly indicate how some more recent treatments of matter and physics relate to this distinction, that is, to what extent they could also be understood as being field or agents' theories of matter in Weill's sense. Afterwards, I shall relate this dichotomy to what one might call the fundamental theme in Weill's philosophical writings of the mid-1920s, and of this book, Philosophy of Mathematics and Natural Science in particular. And this is the gap or tension between activity and passivity, or freedom and constraint, as Weill put it. This tension, not only in the case of theories of matter, manifests itself as the historical saw or oscillation, and the resulting and rather specific intertwining of historical and systematic thought against the background of this tension marks a rather typical German idealist tradition. Hence, I shall end up my presentation by a brief sketch of how Weill aimed at what might be called the philosophy of nature. According to Weill's section on matter in his 1926 philosophy of mathematics and natural

10:00 modern time starts with assuming that matter is substance. Matter was assumed to be, one might say, self-contained and self-sufficient, and it was assumed to be the bureau of properties like mass and extension. However, the development of physics, in particular since the 18th century, showed that so-called substantial properties could be understood in terms of dynamics, and thus without assuming a separate bureau. In particular, this development was fostered the growth and consolidation of electromagnetism. And with this classical field theory, it became tempting to reduce matter completely to fields. A very influential example of such a pure field theory, as Speil calls it, is the electromagnetic program by the German physicist Gustav Mee. Roughly speaking, Gustav Mee claimed that matter was nothing but knots in the electromagnetic field. This was in 1912, and six years later, the next important pure field theory was suggested by Weill himself. Since this was now 1918, Weill could start from a different classical field theory, namely general relativity. Also intuitively, this might be a more promising approach, since one now tries to dissolve matter into time and space instead of electromagnetism. In his philosophical reflection of 1926, Weill showed a direct link between the old Cartesian idea that matter is pure extension and modern pure field theoretic approaches like his own one from 1918. Tempting that this reduction of matter might seem prima facie, already around 1920, Weill became skeptic about it. According to Weill, what goes wrong in pure field physics is that it only describes what he calls a, I quote, silent, continuous flowing of fields, and that it is no dynamic view of the world. Weill, I take it, has two things in mind here. First, after getting rid of all concepts of substance in the pure field theory, there are no agents left, no particular entities acting and suffering in space and time. you like. Second, field theories are invariant under time reversals and so the tension between past, present and future, which we as human agents in the world do experience, plays no role. It was Weill's ingenious move to now solve these problems or to fill in the gaps of a purely field theoretic worldview by means of new results from atomic physics that in

12:30 itself also first looked problematic. Already in 1920, Weill argued for acknowledging the genuine probabilistic nature of processes in the atomic realm. Since for Weill, the use of statistics in physics is based on a notion of cause and effect, and since for him the direction of time is constituted by cause and effect, quantum physics brings time as experience back into the description of nature. However, since electromagnetism and general relativity also are empirically successful theories, and since they describe the silent happenings in space and time, the realm of the quanta cannot be space-time. As far as physics is concerned, this conception crucially depends on the usage of Gauss's theorem in field theory. As Weill himself shows in his paper entitled Field and Matter, Field of Materials, One can transform all relevant properties of matter from volume to surface integrals. According to Weill, this has to be taken seriously, which means that field physics has to get rid of a hypothetical interior of particles and has to content itself with surfaces or spatiotemporal neighborhoods. The fields themselves, then, are caused by matter, but that doesn't mean that matter is really placed within such spatiotemporal neighborhoods. Matter itself, Weyl's helpers, is rather transcendent or extra-mundane. So for Weyl, space-time is not a simply connected manifold, but at least topologically, rather something like a cheese with holes in it. By the same token, Weyl gains room for quantum physics, because quantum physics works in spaces other than proper space-time, sort of space. But at the same time, he leaves the success of classical field physics untouched. According to Weill's agent theory, matter is something which acts and suffers, as he puts it. In this respect, matter is somehow similar to an acting subject or to an ego, and Weill often uses the Fichtian terminology here, speaking of an ego. For instance, state reduction in quantum mechanics is described by Weill's decision-making, Though, importantly, not in the sense that in the realm of quantum physics, matter decides active voice, but that decisions are made. That is, Wael is keen to use passive voice here and to avoid attributing reflexivity to matter.

15:00 Let me skip over the details here and just briefly add that this connection allows Wael to combine the human experience of freedom and the activity of spontaneity of matter and to account for the absolute coincidences in the quantum realm as a kind of perspective effect. Besides, it closely relates to Weyl's idea of an in- and outward-developing space-time, which for him is the only satisfying account of any continuum, be it mathematical or physical, and which is opposed to the finished or tenseless universe of field physics. To put it in a nutshell then, with his agent theory, Weyl aims at the unification of field physics and the newly arising quantum physics. He claims to give back causality its proper place in physics, to get causal experience and the experience of a flow of time back into the description of nature, and to provide a satisfying account of the continuum of space and time. Besides, he claims to have finished the old Leibnizian project of an agent's theory of matter, and indeed, by borrows the term agents from Leibniz. By way of combining the active rearm of, if you like, quantum monads with field physics, which describes only the transmission of forces through space and time, Weill claims to have found out about, and this is a quote, the communication of the monad. Having introduced Weill's dichotomy between field and agent theories of matter, I shall briefly turn to the question whether Weill's distinction between different types of theories of matter is applicable to physics after 1926. So within the second half of the 20th century, a prominent attempt to develop pure field physics was John Wheeler's geometrodynamics. Likewise, unified field theory of 1918, Wheeler's project was particularly motivated by general relativity and also aimed at reducing matter to geometrical features of space time. According to geometrodynamics, what appears to be a mass is basically a lump of electromagnetic energy sticking together by its own gravitational force. And what appears to be a charge is nothing but what Wheeler called the wormhole in space-time through which a bundle of electromagnetic fields lines go and which, if observed from some distance, looks like a charged point-like particle. Wheeler here correctly refers to Beile as the originator of the view that space-time

17:30 However, the problems of Wheeler's approach are numerous. These lungs of radiation are very, very large and heavy, and so it's very difficult to relate them to what we usually think of as being physical entities. Most importantly, Wheeler was only able to elaborate classical geometrodynamics. That is, he could give a geometrodynamic account of classical mechanics, general relativity, and electrodynamics. However, as he himself emphasized, this was only meant as a kind of stage setting for the real project, namely quantum geometrical elements. But this project was only hinted at and could never be worked out by Wieler. A more recent approach claiming to stand in the Wielerian tradition is the fiberbundle formalism in quantum field theory as developed by Hill and Mielke. Since fiber volumes are connected to the points in space-time, but are not themselves part of space-time, this view also has an element in it taken from vice-agent theories, as indeed Mielke explicitly acknowledges. Take for instance strong interaction, which is now described as the geometrodynamics of color space-time. Arguably, this is a geometrical description, but of something that happens beyond space and time, if you like. So, contrary to their own claim, Hehl and Mielke have left at least the exact geometry-dynamic framework given out by Wieler. However, as I like to suggest, according to Weyl's distinction, they do not belong to the camp of the agents theorists, for their approach neither knows of genuine material agents nor does it allow for Weyl's notion of decision, since the fiber-bundle formalism is self-classical. Apart from these two examples, which I mentioned because people here refer explicitly to Weill, also more common approaches in quantum field theory or particle physics more generally can be meaningfully evaluated against Weill's dichotomy between passive field theories and agent theories. But of course then one has to be careful with the notion of field which Weill used only in the classical term. So perhaps let me only mention the two main roles of quantizing matter here. quantum gravity and string theory. Like Weill's unified field theory and like Wheeler's and Mielke's geometrodynamics, loop quantum gravity also is primarily motivated by general relativity and starts from the allegedly

20:00 firmly-based concept of background independence. So in Weill's sense it builds on a rather field-theoretic framework. In contrast to this and rather similar to Weill's agent theory, string theory starts from a more general speculation about what matter might be, other than just curved spacetime or assumed test particles. And it starts also from a more general speculation that this matter is not necessarily or outright from the beginning placed in our four-dimensional spacetime. It would be tempting here to discuss the transcendent of matter further and, for example, related to the role of what is called holographic principles, both in Bayes agent theory and in string theory. However, instead of speculating about this, I shall come back to Weil and to how his description of different theories of matter is part of a bigger philosophical picture he wants to draw. going back to the conceptual frame of wild historiography of theories of matter a certain dialectic structure is apparent putting it very roughly in their pure form both substance and fear theories of matter although being opposed to each other cannot provide a satisfying dynamical world view according to Wiles. Substances, in the classical philosophical sense of the term, do not interact with one another, and pure field physics knows of no dynamic agents at all. Those views are then, as one might say, preserved, aufgehoben, in an agent's theory with its dualism of matter and field, and Wiles' resulting concept of communicating moments. As Weill is keen to show, the difference between dynamic views, which take matter to be an agent, and passive view, which try to dissolve matter into geometry and field, shows itself as a historical seesaw or wavering. According to Weill, this wavering can also be described as that between freedom and constraints, which fundamentally characterizes human nature, for humans are both spontaneously acting, intelligent beings, and also bound to a physical body. Having this in mind, it is perhaps easier to understand Weil claimed that with his notion

22:30 of decision spontaneity enters the physical reality, how thereby matter becomes more like an ego, and how on the other hand he talks about field physics as, quote, strict law unquote, which is only able to account for the, again, quote, silent flow, unquote, in four-dimensional space-time, but not for such crucial concepts as lies. Indeed, one should take these remarks seriously, in particular, since Weill himself says that it is the tension between freedom and constraint that marks the driving force of this whole book, Philosophy of Mathematics and Natural Science. And one can easily see this also by looking at what Weill writes, for instance, about the notion of continuity in mathematics, which, as I already mentioned, is also intimately connected to what he thinks about physical continua. As in the case of matter, Weill here presents a conceptual development as a seesaw process between passive and active views, views that take a mathematical continuum to be something given, as for instance in set theory, and views according to which a continuum has to be actively constructed by the mathematician, as for instance in the case of Brouwer's free choice sequences. So this example might be a little tricky. For Biel, the vaporing between freedom and constraint as a historical process can be found in all major areas of mathematics and physics. This and the way he presents this intertwined systematic and historical consideration turns his 1926 book into something like a philosophy of nature. And it shows Biles' reception of German idealism, in particular of the writing of Johann Gottlieb Fichte. Apart from the historical and autobiographical evidence we have for this reception, it can be seen, for instance, from the way Vile attributes its activity, but not reflexivity, to matter. Vile is very careful here not to turn into naturalism or into a Schelling-type natural philosophy. Vile rather states with the Fichtian slogan that one should attribute as much activity to nature as possible without turning nature itself into a self-aware subject. More specifically, Weil himself writes that by looking at the historical wavering between freedom and constraint, one recognizes that, quote, there arises a third Riau, unquote.

25:00 This Riau is that of what Weil calls symbolic construction, and he states that it was, and again, these are quotes, it was the born and bred constructivist Fichte who first enters this Riau. To me, Weil's constructivist and in part pragmatist reading of Fichte seems to be a sensible and much more interesting alternative than the today unfortunately rather standard reading of Fichte as a philosophical foundationalist interested in some rather mystic self-relation of the ego. In contrast, I suggest that by telling his oscillating history of, for instance, the the concept of matter and of the mathematical continuum, Weil schaut the historical dimension of what Fichte calls, and now I quote Fichte, the wavering of the power of imagination. Da schwebende Einbildungskraft, unquote. By the same token, Weil fulfills, at least in part, the Fichtian program of philosophy as being the, and again this is a quote from Fichte, pragmatist historiography of the human mind. End of quote. I hope this look at theories of matter could illustrate Weill's philosophical framework around 1926. With this concept of wavering between activity and passivity and of an arising third rearm, Weill tries to interpose himself between Hosserlian phenomenology, which he pretty much adhered to until about 1920, and Cassira's philosophy of symbolic forms. For Weill, phenomenology, with its key concept of viewing essences, was now an altogether too passive view and Casiera lagging a strong or proper concept of life was in danger of being a kind of idle running activism. So using the Fischian term which is meant to express exactly the two-sidedness of life as activity and passivity, one might say that by posits himself between Husserl and Castellanos. Thank you. Thanks. So, questions? We have about ten minutes.

27:30 I didn't really understand this activity and specificity. In what circumstances do you call something effective, and in what circumstances do you call something effective? I can understand it from a philosophical position, you have believed in the musical skills, but if it was a musical, what does it correlate? In Weiss, in the case of Weiss, it pretty much goes along with the notion of decision. If you look at his agent's theory, he thinks that their space and time really develops, that space and time itself gets more fine-grained with every decision on the quantum level. So it's with the notion of, so okay, you might say it's a philosophic notion, but that's what you connect to the activity and then you have a kind of process where you get not only, as time develops, not only time goes on, but also the past becomes more fine-grained because of the decisions and so the matter does something. I think that's what goes together with this idea of this outward and inward developing of the continuum, but not so much with something you can exactly point to in a physical formalism. Sorry about that. I don't think that he says at some point, and this is really the point in my formula where we have the activity, but part of the problem is of course that when he writes this, I mean, quantum mechanics is not valid, so he has this kind of vague notion of decision, but that's the kind of thing I would point to. This notion of decision is metaphorical or not, the second point involves thinking.

30:00 I believe that nature, that the whole of it is passive, while it's only the psychological that can be active, or am I wrong? Okay, so as for the feature, I mean, of course, Wiles takes feature, say, as a cultural resource or something. I mean, he's no orthodox feature, as he never was an orthodox to serve anyone. And so, I mean, I think what he does is you can repeat. I mean, there are projects that have tried to work on what would be Fitch's philosophy of nature. And of course, I mean, the ego is always constrained by the non-ego. And if the non-ego is nature, I mean, you have this kind of certain feeling of resistance going in there. So it depends on what you think of that. So that was that part. And the other thing is with the notion of decision. But then, as I said, I mean, he's at least keen, I mean, he tries to hint at the difference. I mean, he doesn't say that Quanta decides something, but in this reality, decisions are made. And this, I think, is kind of interesting. And it's also why I think it makes sense to take him as adopting a more Christian tradition and not say naturalism or not kind of shedding time and saying that that method is hard. And so about the same time, if you think of Whitehead, I would say that they're both divided. I mean, there's kind of a lot of common interest, but definitely a request when it comes to naturalism and to the notion of opposition, which is also quite prominent in White, and then they're both active, you know. Okay, well, I think we should thank the speaker again, and then we'll move to the next session.

32:30 Okay, so the next speaker is Dennis Henkel from Oxford, whose title is Geometrializations It's running. And I've just seen it working before we all came in. I tried to use FI to make any use for it. Which one? Well, but the thing is, I don't even see something on the screen. Oh, close. Do you think we should restart it, or do you think we should restart it? I don't know. Try it, I mean. Maybe that's why you wake it up anyway. There's no connection between that. Yeah. There we go. There we go. Okay, so perfect. We know the next one. What's the message?

35:00 I'll only speak about part of what I originally wanted to talk about, hence a different title. In particular, I will speak about the concept of matter and that's the general relativity and how it relates to geometry. So if we look at the Einstein field equation, we have the energy, we have the Einstein tensor formed of the Ricci tensor and the Ricci scalar on the left hand side which are both ultimately formed of the metric field and its first two derivatives on the left hand side and we have the energy momentum tensor on the right hand side. So what does this mean? Famous way of putting it It goes back to John Mouline who said the equation means matter tells space-time how to curve and space-time tells matter how to move. And one way of interpreting this sentence is to say, well, the left-hand side is supposed to represent the geometry of space-time, the right-hand side, the matter content of space-time. And if we change something about the left-hand side, if we change the geometry, then the way meta is distributed on moves changes as well. And on the other hand, if we change the meta distribution, the geometry of space-time will change. So implicit in this seems to be that we regard the energy momentum tensor as in some way directly representing meta. And here's a quote by Friedman, who made the same claim, explicit, saying, in a relativistic context, the proper representative of matter is not the mass density rho, as in Newtonian physics, but the total stress energy density t. And my talk will be about two questions. The first question is, is it justified to regard the energy momentum tensor as representing matter in any direct way? And the second question, connected to that, is whether the left-hand side of the equation fundamental are more basic than the right-hand side. So it's geometry in some sense more basic than the energy momentum tensor. And traditionally, the other route was taken. Right up till 1922, Einstein was a believing follow-up what he called mass principle, which in his formulation says

37:30 the metric field is fully determined by the masses of bodies, since according to the results of the special theory of relativity, mass and energy are the same, and since energy is formally described by the symmetric energy tensor T, Musk's principle says that the metric field is constrained and determined by the energy tensor. Now, famously, GR doesn't fulfill this version of Musk's principle. For every energy momentum tensor, in particular for T with zero, we can find many solutions for the metric field, for t equals 0, most famously the McCoskey solution, and different solutions corresponding to a space time in which only gravitational waves are present. So it's true that the metric field is constrained by the energy tensor, but it's not determined by it. Right, but also here, one way of the is to say it seems that the energy tensors are supposed to represent matter in a quite straightforward way. And the first question is whether that's justified. In order to tackle the question, I will first point out how an energy momentum tensor is structured. So I present the common scheme that every energy momentum tensor follows, then describe two paradigmatic energy momentum tensors to get a better feel for it, And then go on to ask what mass energy momentum really is, pointing out that it's a kind of property. Then ask what kind of property is it, a property that only belongs to matter, is it an intrinsic property, or is it something else? All right, so first take yourself an energy momentum tensor. Here's the scheme which every specific energy momentum tensor, every specific tensor supposed to describe the material system products. We have as a T00 component the mass energy density, and then here the free vector describing the momentum density, free vector describing the energy power density, and here in terms of describing the momentum power which is equivalent to the stress tensor as we needed in monolithistic fluid dynamics. And all of these components can vary from space time point to space time point.

40:00 And so the most adequate way of describing or of naming T would be to say it's the mass energy stress tensor density. But in order to make it easier, I would just call it energy momentum tensor or even just energy tensor for short. All right, two specific examples of energy-momentum tensors. The first paradigmatic example is the perfect fluid. So this is the energy-momentum tensor of the perfect fluid, where rho is the mass energy density of the fluid, p is the pressure that parts have another part, v is the velocity of the fluid. Here again, the pressure, and here, maybe surprisingly, we find the metric tensor. within the energy-momentum tensor supposed to represent matter. And one of the main questions later on will be whether that is just a mathematical fact or whether there is actually something behind G occurring in the energy-momentum tensor. Here's the second example, the energy tensor of a free electromagnetic field, where we again have the metric tensor in there, and the other main ingredient is the Faraday tensor, or electromagnetic field tensor, whose components are given by the classic electric and magnetic fields. Right, so now to the question, why is T important in the first place? What do we need it for? The answer is, for all paradigmatic material systems, knowledge of T and the assumption that T is covalently conserved, So the generalization of conservation of energy, momentum, and mass is sufficient to determine the equations of motion or field equations of the system in question. So for example, if you put the electromagnetic energy momentum tensor that you just saw into this equation, then you get the Maxwell field equation. If you get the energy momentum tensor of the perfect fluid in there, then you get the classic Navier-Stokes equations. However, one should be careful in claiming that the equations of motion of motion are the way they are because of this equation. In a way, it seems to be more general to claim the other way around. Given the equations of motion, I can also deduce that energy momentum must be conserved in a way this is a more general claim.

42:30 However, in practice, we often have the energy momentum tensor not knowing the equations of motion. the energy momentum sensor because we know the left hand side of the Einstein equation, then get the energy momentum sensor and then deduce the equations of motion from the vanishing of the cobrane diversion. So, quite important to practice and in terms of foundations as well. So, but what is it? What does it represent? Here's again my principle, which seems to to claim that T represents matter in a direct way, and I've already pointed out it's not fulfilled in J.R. However, at least at a first glance, it seems that something like an anti-Machian principle is fulfilled in J.R., which would say the energy tensor T is fully determined by the metric field, because if we know the left hand side of the Einstein equation, the energy momentum and those uniquely determined. But claiming this is a direct counterpart of Mass is the book goes a bit too far because we can ask is T really representing the properties of matter in the same way as a metric field and the tensors formed by its derivatives represent the geometrical properties of respect time. And in order to answer this question, so are they on the path T and G, or are they not? And in order to answer this question, let's look at two options. Option one is that T represents all the properties of matter, allowing us to regard it as a direct representative of material systems, at least in classical physics. Option two is that T represents a property of matter, but there may be others that are not included in the energy momentum test. And then later on will come the question, what kind of property is it? In order to answer, to decide between the two options, let's look at some results that have been obtained by Tata, if you have to go. The question was, how do we know what kind of matter the components of T belong to? Or to put it differently, can the energy tensors of two apparently different matter configurations be identical in that they have precisely the same components and at the same time satisfy the Einstein equations for the same metric field? And the answer is yes. for the components of a given metric tensor giving us the components of an energy tensor, it is possible that from this one energy tensor we can derive both

45:00 the Maxwell's equations and the equations of motion for a viscous fluid. What does this mean for our two options? If we take option one saying that he represents all properties of matter, then this would commit us to saying that there is no physical difference between certain viscous fluids electromagnetic fields. We may not like that, but we may, you know, fight the bullet. But there's an additional problem because even if we say, okay, they behave in a dynamically equivalent way, this still doesn't mean, this still doesn't mean that they have the same kinematical possibilities. The state space must still be the same, even if the equations of motions are equivalent. And so, well, that's quite a problem for this interpretation. On the actually to saying that the energy momentum transfer represents only any property of matter then we're much better off then we don't then the tougher results only mean that two different matter configurations can share the same property and that's this will not be surprising it's the same as saying an elephant can be read a mouse can be read but that doesn't mean that mouse that red mice and red elephant are the same thing same thing so option two seems to hypothesis when matter is represented by the matter field's side, like the electromagnetic field that occurred in the energy momentum tensor of the free electromagnetic field, and every matter field has an energy momentum tensor associated with it, representing its mass energy momentum properties. And we'll see how, whether this hypothesis works well. So given that we take energy What kind of property is it, and is it really a property of only matter on intrinsic property? And in order to answer this question, I want to have a brief look at Lagrange and fear theory, which gives us a general account of the equations of motion for a classical system, and at the same time, the possibility to give a general definition of an energy momentum in terms of any system, any system containing matter. The basic idea of Lagrangian theory is that every physical system can be characterized by Lagrangian entity L, or Lagrangian for short, with the L of which we can define an

47:30 action S. And setting the variation of the action to zero gives us the Euler-Lagrangian equation. And from these Euler-Lagrangian equations, we can obtain the equations of motions or a few equations for any classical system. So maybe in a way, at first it may be surprising that for all classical few equations we can re-obtain the equations of motion from this equation, but also for new ones it works. So if you put this Lagrangian into the Euler-Lagrange equation, the Einstein-Hilbert Lagrangian, then you get the Einstein vacuum equations, i.e. the Einstein equation with a vanishing momentum, energy momentum sensor. And on the other hand, if you put the elect, this Lagrangian into the Oller-Lagrange equation in which you have the metric and the electromagnetic field, then you get the sort of the Maxwell equations. Right, now let's look at what happens if we take the total Lagrangian to be put into the Oller-Lagrange equation, to the summation of the gravitational lichongen and the electromagnetic lichongen. Here again, variation with respect to f, with respect to the electromagnetic field, gives us the source three Maxwell equations, whereas variation with respect to g gives us the so-called Einstein Maxwell equations, where we have the Einstein tensor here, and the energy momentum tensor is given by the energy momentum tensor of the three electromagnetic fields. And this equation is equivalent to saying the left hand side is the function derivative of the gravitation and the perspective metric, and the right hand side is the function derivative of the electromagnetic with respect to the metric. Now we may ask, well, what's the reason, given that we integrate this as the energy momentum tensor of the electromagnetic field, why don't we integrate this as the energy momentum tensor is here, what keeps us from doing that. And what keeps us from doing that is a difference in dependence. The gravitation Lagrangian is the only Lagrangian which only depends on its own field, which only depends on the metric field and its derivatives. Whereas every metal Lagrangian, for every metal field side, the Lagrangian depends on both the

50:00 matter field and the metric and its derivatives. So there's a clear-cut mathematical distinction If this were not the case, then varying M with respect to G would not give us anything interesting, let alone an energy tensor, because it would just be zero if we didn't have this dependency. And hence, it seems the main property of matter, mass, energy, momentum, angular momentum, the main property of matter depends on space time by the Lagrange depending on G. And the of the general energy momentum tensor in turn. In a way, maybe this is quite natural. We can define an empty space, but we cannot define matter or energy that does not live in, with, or on space. Whereas this statement is a bit of cheating, because we can define the matter field without respect, without referring to the metric field, but we cannot define energy without doing it. So to look at the whole issue from a slightly different Imagine we have a system consisting only of a scalar field psi and an electromagnetic field F. Then we have two possibilities above what the total Lagrangian of the system sees. Either it is just the sum of the free scalar field Lagrangian and the free electromagnetic field, so the two are just living next to each other without interacting. Or the total Lagrangian is the free scalar Lagrangian, the free electromagnetic Lagrangian, in which the electromagnetic field and the scalar field coupled to each other, i.e. are multiplied with each other. But now, if we trade one of the meta fields for the metric field, then these two situations are equivalent, because our definition of what it means to be an interaction part is fulfilled by every meta-lagrangian with respect to the metric. There is no metalagrangian in which the metric field doesn't throttle to the matter field. So it's not possible to have matter without it coupling or interacting with the metric field. Space-time is always there, so to speak. What do we conclude from this? First conclusion, mass, energy, momentum is not an intrinsic property of matter, because

52:30 in order to define it, we need the metric field as well, and not just the matter fields. In order to recover our everyday concepts of matter, in which matter has mass, energy, and momentum, it's not enough to speak about the fundamental matter fields. We need the metric field, the space-time field, to do that as well. And so, mass-energy-momentum is a relational property due to a relation between matter and space-time, having a map from the metric field and the matter field to energy-momentum tensors. So this is the relation, and the energy-momentum tensors is the relation of property arising from that. A bit like brotherhood is a relation between me and my brother, and giving rise to a property, maybe me having a brother, which I just couldn't have if that wasn't this other guy, fortunately. And, yeah, so math and engine momentum seems to be a rational prophecy. All right, that's it. Again, there's quite a bit of time for questions, if there are questions. Yeah, that's a good question. That's quite controversial. So the question is, why don't they have an extra term here involving the cosmological constant, which would be lambda times GAB. And I think, well, it's an extra issue, basically. And it comes, it's an extra question, and the question is exactly the one your, your second question. Would the gravitational constant, should it be regarded as part of space-time or part of matter? and I've just been to a conference by cosmologists a few months ago and there it was quite controversial half of them wrote it on the right hand side half of them wrote it on the left hand side which you can of course always do it's just you know you bring it to one side and the others bring it to the other but it seems to be very controversial should we regard it as some vacuum property of matter

55:00 an energy of space one or should we regard it as an additional kind of matter and you know some just refer to it as dark energy but it is controversial i'm not sure i don't have a final opinion on it you said that energy momentum is the elation the matter on the one hand and the Yeah. But how, in that equation, do you characterize matter without any dependence on space-time? So this Psi, what is it? Oh, that's a placeholder for all kinds of matter fields. So scalar fields, electromagnetic fields, all kinds of fields could be put into the Psi. Yeah, the meta fields can be defined independently of the metric field. It's only the manifold. Oh, I see. But the meta fields... So what are the components of these meta fields? Depending on the situation. If this meta field is the electromagnetic field, then it's just a power bay tensor. It's a scalar field. And so it doesn't involve g? Okay. That's why, to come back to the original question, in how far is matter geometrised in GR? It's not. One of its main properties, maybe the paradigmatic property, is connected to the geometry of spacetime. But the notion of matter as such is not. And if we then go to generalizations of general relativity, like the ones Norman presented, then we have the additional step that the matter fields tried to be incorporated into the geometrical framework. So, for example, in Bayard's theory, the matter fields are derived from the connection compatible with the metric, and so there in a much stronger way, we have a much stronger connection between matter and geometry, namely, matter is, the matter fields themselves are geometrised in a sense, which we don't have in GR. Dennis, I have a question for you. Can you go back to the Tupper results slide you have?

57:30 So can you expand a bit on the second bullet point, you say that the components of a given metric tensor, so we've got the components of a, we imagine the components of the energy tensor given, it's possible from this tensor to derive both the Maxwell equations and the equations of motion for viscous fluid. From the from the t so you have the metric first put it into the left-hand side of the Anton equation thereby find out about the right-hand side giving you the components of the energy momentum tensor and then from the covariant derivative of this energy momentum in terms of giving certain constraints, you can derive both the Maxwell equation and the equation of motion for the fluid, but there's strong algebraic constraints on this possibility. So it's not the case that, it's always the case that the Maxwell equation, that for any electromagnetic energy momentum, you get the Maxwell equation to be equivalent to the equation of motion for the fluid, it's just for certain, for a subset of those. So, I mean, I'm quite puzzled about this. So, one very unsurprising result would be that for two very different kinds of material systems, maybe a system of Maxwell fields and a system of viscous fluid, the equations are such that you can have identical solutions in terms of the geometry and the mass energy distribution. That, in a way, wouldn't be that surprising. I mean, it's kind of a genuine substantive result that it's possible. But there, you're thinking of the mass energy distribution as a tensor and just a bunch of numbers relative to a particular coordinate system. Now, to get from the energy tensor to equations, you've got to think of the energy tensor as the components of the energy tensor as given, you know, as having some functional form in terms of certain other fields. And then it's from that fact that you work out the equations of motion for those fields. But then I don't see how you can on the one hand have the components of the tensor being the function, you know, functions of some fields, so that when you exploit the fact

1:00:00 that the divergence of its vanishes, you get the Maxwell field equations. But then for, at the very same time, you've got the very same tensor, but then you get out. But is that really what you're claiming? Well, up to a certain point, yes. What's not the case is that you have to put in, given that you have the components, what you don't have to do is then to put in the assumption that, well, now let's assume it's the energy momentum tensor for fluid, and therefore we have mass density, pressure term, and velocity. So you don't have to put that in, you get it out, you get the equation of motion which you can then show to be mathematically equivalent to those in which you start from the very beginning from an energy moment in terms of which you assume you have method that we have special data and so on. Thank you. Oliver? Yeah, it's a little bit dense on this point. It doesn't really need a school suburb for his purposes. It only needs to say that an energy cancer can represent one and the same energy cancer. It can represent this thing and that thing at the same time, which is, as you say, not surprising really. then it's this we can derive, you know, we can derive from the tensor equation is something that some may need for this purpose, but you don't really need it. Well, I'm not sure, because in order to say or in order to justify the claim that this one energy momentum tensor represents, can represent both an electromagnetic field and a viscous fluid, the justification for this claim, or at least one strong justification, It can't exactly be that from this one, you want me to say, Yeah, we're right. You give me, you give me max correlations, and you give me some big fluids, and then just to write the tensor and find out that it works. But that's, so you mean, but that's not, that's not saying the equivalent yet. Then, then you have to show an additional step showing that, that it stood, uh, to equivalent tenders that you get all of that. Yeah. Great. Well, you're okay, but then you just do it the other way around, the Tava wants to do it, that's fine. Okay, are there any more questions?

1:02:30 One question, can we summarize what you said by claiming that the matrix field has a principle, why does the trace energy have relation? I would say, if we want to, I think most sensible would be to say the metric tensor describes intrinsic properties of space-time, and the matter fields describe intrinsic properties of matter, namely the way matter is distributed, and from these two fields we get a relation of property which is in a sense a I think it's not exactly the same, but I don't want to cut it. Okay, let's thank the speaker again. thank you Thank you. You want to be a problem with me?

1:05:00 is it is it just you okay well the next the next speaker is eric um from um and he's talking on joint work um that he's done with gabrielle and coco The title is Relativity Theory and Poincaré's Conception of Spectrum. Our main concern is a following issue. D'Afenstein and General Relativity entails the theory of anti-conceptional space. For us, when one appreciates currently the differences between the conception of space of these two authors, the answer is negative. To illustrate and to introduce women, our work in Portuguese is at this difference Lines between Poincaré and Einstein lag on philosophical, namely ontological, commitments. To illustrate and to introduce this work in the study, let's consider the more familiar case of special relativity. Since it is mainly through the analysis of the respective contribution to what is today considered as physical and special relativity, that Poincaré and Einstein stand-alone is being compared. He is now generally organized that both theories are physically innocent in the same language, namely this is the end of the term of the rational consequences. Nonetheless, some important differences exist between the two approaches. The very fact that, for a long time, physicists and historians believe that Poincaré missed special relativity evidence of such differences. More, it is well known that Poincare never accepted Einstein's

1:07:30 special rights duty, even if he recognized that it shook for a short while in his conviction. Now, the historical description of the genitals of both theories gave a full account of the differences between Poincare and Einstein. But to now, they bet. Mainly, the following explanation has been proposed by interpreters. Firstly, Poincaré never get over the step to the spectrum of Einstein's special reality because you have to conform. Poincaré proceeded as a mathematician, whereas Einstein proceeded as a fixed step. Thirdly, Poincaré's epistemological remarks are no safe pride for the study of his contribution to physics In our view, each of these interpretations is erroneous. The differences between the two approaches have to be explained by the different ontological commitments. Volker is ground on the self, Einstein's one, on the repartition in the space of the plurality of empirical subjects. Moreover, to confirm the comparison of Poincaré and Einstein's epistemology to special work would be misleading. it would take Einstein's different from the right direction of Gelsch. Secondly, it is easier to step to what is Poincaré's theology than to step to what is Einstein's mind, because the father was the same Jews from the early 90s up to his death, whereas Einstein changed his view several times. or plane, will be the following. In first, we discussed briefly the most general acceptable agreement used against Poincaré and here, that is the issue of the constant curvature of space. Secondly, we sum up Poincaré, no space, no motion in conception, which is the ground for the of its main issue, and which opposes the entire Einstein-Otheraist's notion of motion.

1:10:00 We will conclude in the last of the previous discussion by comparison of the relationship between physics and cosmological ideas in the production. According to Poitier, space for physics, which is not physical space, are to be of constant curvature. Seymour also had different times, arguing that in general relativity, arguing that in general relativity the curvature of space changes the distribution of matter, and therefore that this curvature is not constant, compute the criteria's own perception of the role of geometry and physics is forth in principle. Nevertheless, such a conclusion is incompatible with Einstein's view as presented in Geometry and Next Edition. Geometry and Next Edition. In his essay, after that Poitier's physical-geometrical algorithm is, in principle, irrefutable, Einstein emphasizes that it could never have formulated reality in theory without accepting the autonomy of practical geometry, opposed here to pure geometry, which, he says, is the most ancient of the physical science. After opposing his point of view, Solgier X, Poitier 1, Einstein's This idea of particle geometry extends to spaces of cosmic order of magnitude using, with some simplification, the same term here encode, in the New World paper, Reflective Cosmology. This discussion concerns the problem of knowing if space is flat or spherical. It is important to stress that for each of the considered possibilities, space is first three-dimensional to either of these three-homogeneous.

1:12:30 Thank you, Einstein's discussion is about space of Confident's Coventure, which is to share one another only for the fact of the Confident's Coventure. The above mentions, authors pay no attention to very important distinction, the one between equations of general relativity and exact solution of the equation. Every observation or confirmation of general relativity equation obtains with approximated solutions, where the general form of space is indifferent. For this reason, strictly speaking, one cannot of general relativity theory, because here we have a mixture of theories, namely, special relativity space time and general relativity particular volatility. Or, to put it in as a way, in other words, a theory found in 16 is an incomplete theory of gravitation. It from a frequent compute, an expression with a pattern in general gravitation. So, to get rid of this infiniteness, the exact solution of the field equation is required which will give both the progression in the shape of the world universe. Since there are infinitely making any exact solutions compatible with Einstein's equation, Then, there are, in the 50th, cinema-replicit series. This is a reason why we concentrate on Einstein's one, and need to fix a term of this.

1:15:00 What would we say later in this, in the 50th, cinema-replicit series. Second part. One of the most peculiar aspects of planetary conception of space, differentiated from Einstein is a fact that Poitier recognized the existence of geometrical space, object of pure geometry, and the existence of what we call the repetitive or sensible space, but it denies any kind of existence to physical space, namely to the object of an Einstein and practical geometries. Representative states the framework in which we represent our own body and our body surrounding us, which is not an accurate form of our intuition, but a complicated constriction coming from the interaction between the structure of our sensations, the data of our environment coming from our different senses, and the notion of movement which is inspired in our lives. In turn, involuntary and muscular sensations plays a fundamental role in the formation of the robotic space. Transcendental international movement is not critical of the insulation or of the integration. In the center of all the external changes, we need to find movements of change in class or space, and through the changes that they decompensated by receiving a running chair mascara in session. is an object that if there were no rigid bounds in our underwhelming, no external changes could be compensated, and the construction of a represented space could be imperfect. Geometrical space is the mathematical structure that continues to speak about the differentiation of both into reason to reason about the geometrical relations between them to fix an objective notion of distance.

1:17:30 Pure geometry is the last and first theory of global transformation, but not all kinds of global transformation will prevent constriction useful and educableness to our experience. The notion of movement can be represented in geometrical space, only in space as a constant correction, only because it stems to the form of the future, then the motion of an invariable future can be represented by in fact, the possibility of a motion of an invariable future is not a separate line too, at least it is evident in the way in which the practice of spiritualism is evident, and not an analytic aqueolation routine. More on that on quotations too than not. There are two important consequences of respect. Firstly, what I have talked to in of the constant curvature of space is not a green mark in my face, It is a necessary condition for the application of geometry. What does this mean? It is certainly true that, like what I say, if there were no further body in nature, there would be no geometry. But the unparalleled origins of pure geometry do not imply the possibility of identifying geometrical space with representative space. space and non-reflective space are very different in their artistic progress. Born like in the quotations four and five in their marks. Now, seems to be, to be known, there is no physical space besides presently in a geometrical space. That means that there is no frame in which the physical motion, motion of the back, is within space. All we need to do physics are our sensations, and imagination, and structures in our present space, and visual and physical relations, which are objects of reason and not of reality.

1:20:00 The inner state of the inner state of the physical space is related to portray a specific negation of any kind of absolute movement. not only absurd movement in its own sense, but also of any kind of surrogate of its absolute movement like, or in science, movement where I think there is. This phrase is expressed by the way of the fact of the sky and the purpose of the motion of the air, and the fact is that motion is not something really in itself, is also confirmed by the interpretation of the idea of the Newgerson-Morley experiment. More than that in quotation six and nine, especially on the behaving of a strong principle of relativity. Why such a rejection of the rematch of motion and why such a prediction? Chapter five of science and hypothesis providers is a complete explanation. changes of quality and changes of space and space of the prosperity of compensation in a relative space has no objective meaning in physics, independently of the purpose of the conventional choice of a direct or frame. This is so because when we measure a constant in physics, we need a matter of thermo, and in the compact system composed by our thermo in the body that we measured, we have no way to discriminate objectively between a change of distance or a change of any other physical magnitude. This is the very meaning of Poitier Geometrical Physical Policy. It depends on of the structure of our experience, it depends on the fact that we don't have any nutrition or resistance between two bodies, it depends on the fact that even if in nature there are really rich investments, we have no need to organize them. Therefore, now let us have some change, the change of distance we have with motion of writing such and such. We need before to achieve this season to give much more compassion which is a joint work frame for the description of them.

1:22:30 I'm sorry. This conception is a way to Einstein's one. Firstly, Einstein allows the This button, circle me, and Stein admits that he's right down to us with movement, or an ethereum. Through the head, this is rotation. You can see the end of this rotation is going to take a step forward. The electricity theory is easier to read in the hangout. For Einstein, physical space exists. For Poincaré, such an existence is a showrunner. Space is just a phrase that includes nature. It stands for the local nature, and there cannot be compared. The fact of origin could be made through the alienation of the relationships of mathematics and figures. See, here, we have a community, and when they label it, we should run into existence in relation of figures. But in our science, in fact, we just began confusing the question of alienation. When, Einstein said in the 1928, I began to reflect on the racism, more or less likely than the law, but the problem of gravitation converted me into reading rationalism, that is, to someone who searched for the only real world source of truth in mathematical authenticity, it just means he became coerced when I spent both.

1:25:00 Thank you very much. and to solve the potential problem. In chapter 30 of relativity, it presents the need of such a transition in another way. Usain's theory, he says, requires that the universe should have a kind of sensor in which the density of stars will be the next one. And with this tension, though we enter, there is an infinite vision of emptiness. The stellar universe ought to be a planet island in the infinite ocean experience. As where, Melchior, Einstein had to take in time with this idea of the change of the world, which was present in the 16th memoirs, is not in principle better than the older Einstein memoirs. But we heard the phrase, the first one, the first one, the first one, the first one, the first one, the first one, the first one, the first one. Here, Einstein would get freed of any remnant of asofianism. I raised the predisposmology goes this way. It started from sentation and went through Metaphysics, finished with Metaphysics. Descartes, the founder of modern science and philosophy, turned the scheme upside down. This opposition between the two philosophies that turned out Descartes is similar to the one with the Einstein equation. The nature, like the chart, starts on cosmological ideas that defines a particular range of things. This doesn't mean to propose any cosmological model. On the contrary, from the very fact that we really have a very small part of the universe,

1:27:30 how can I compute that even with the most distant parts of the universe influence local phenomena, transformation is impossible and this is impossible to be impossible because physics ought to be physics or iterate systems The believing rationalist Einstein began with time rather skeptical about the development of of relativistic cosmology. But never all the view that it should be reduced from cosmology. This is why relativistic cosmology, not only ancient one, in the panorama of the 20th century cosmology, has been wanting to name inductive cosmologies to oppose the inductive cosmologies of men, all that are in the world. This picture is clearly a red line of aristocratism, which is already consistent with the rationalism brought by intellectuals. Maybe this list then wiser than Baker's origin, since it's back to Dr. Hay. Okay, do we have questions? Before the beginning of section 2, you said, and later on, I think again, you said that GR in 1916 is incomplete because, well, if I was to be correctly, it's incomplete because we don't have exact solutions yet, and once we have exact solutions, then we have separate theories for every exact solution of the original equation, right? I'm just not sure why this Because, I mean, isn't it equating two things that are more likely at the fundamental equation of 1916, which is there and don't change, and if there are solutions to the equation, each of them describing, or not each of them, but some of them describing the cosmological model, why does this make a 1916 equation incomplete?

1:30:00 That's the right question, the theory, because don't forget our usual problem. Some people say that what a constant curvature of space is being dismissed by general relativity. Okay, I see the main problem, that what is paid by Einstein for general relativity is the extreme number, okay? Einstein said that the one, it was not satisfying because you, to remove the problem of play, Einstein, he used a frame of the special reality. So it's not, then it's not, okay, and the determination of what is in the earth, the issue is in the earth. In gravitation, what is in the earth of the body which is more and more different from every body, but it's not. But so, in the future of the world, because there is still a center of the world, I think it's about 16 years from now, the framework is in the United States. But you could not let's say that Einstein has suggested a more general framework, that he allows for spaces with constant temperature, and he doesn't demand that spaces with constant temperature. One solution of the IHF equation is for Pocheree, it's only the spaces with constant temperature. Sometimes, you don't need to do a question in Chicago. What do you have to do in physics? And in my opinion, the topic agreement is that and now, for instance, it's not the idea. It's not the idea. But then we agree with that. And then actually, next week, next week, next week, next week, next week, next week, next week. The main point is when you start to see the question, you know, it's a very special issue. Well, you open the solar box, okay? And if you make information, you can say, but in which one you will do what? I don't really know. Anyway, so, I thought that I tried to make sure of the three inches of the skin.

1:32:30 So, why can't I say that the general government is going to go back on the service? Can I just quickly ask about your claim? I mean, I take it that it was a kind of, it was bad for Einstein that he was more like Aristotle than good for Poincaré, that he was more like Descartes. And Aristotle was characterised as starting with sensation. I didn't quite understand why you couldn't actually characterise Poincaré in that way. I mean, he certainly doesn't go all the way to cosmology. He'll say, you know, you have to stop. It's impossible to go a certain way along that. kind of set of arrows that he drew, but the way you characterise Poincaré's, the way he defined representative space, that sounded like he was starting exactly with sensation and certain, you know, principles of the way you could theorise about sensation. Whereas, the way Einstein, what Einstein ended up doing was exactly kind of... Thank you.