3-spaces & Machian relationism

0:00 Space time, should we believe in space or space time as an entity separate from the material things that we get out of direct experience or not? And in particular I want to talk about the hard forefront of relationism and Machianism and recent work approaching the idea of Machianism and general relativity from a free space perspective. If you look at the bottom, you'll see that this talk was inspired by two papers, really excellent papers, written by Oliver Pooley, one of them Harvey Brown, both on the Hillside Archive of Pittsburgh, and on both final rehabilitating relations. So in this talk, I'm going to take a critical look at the three space-based approaches to Machian relations, and in addition to repeating some of the things that Ollie said in his papers, I'll be criticizing So let me just get us going by talking about relationism. What is relationism? In a 1998 paper where I tried to defend the idea that these categories of relationism and absolutism, relationism and substantivalism, are not outvoted or outdated ideas, I argued basically that the core idea behind relationism is just a rejection of absolute space. So what does absolute space say? Here's a misstatement with northeastern quarters. Absolute space means that some individual points vary in a fairly tolerant way. So what absolute space or space-time is, like Oliver said, is the right way to point out that the sort of reality and existence in all the multiple aspects of the Clark debate is distinct.

2:30 And Clark should have agreed with Leibniz that... What are the space-time structures? Well, it could involve position. In something like an Aristotelian space, the center of Europe is a privileged absolute position, a kind of spatial structure, but not in Newton's space, of course. More traditionally, velocity and acceleration are the kinds of quantities that a relationist wants to say are not absolute, but have to be understood in relationist, acceptable terms. Assuming that Euclidean geometry is all there is. So real relationism, and again this is a little bit of terminological insistence, real relationism should be the claim that physics can be done without presupposing any of these absolute quantities. The trick is to make it work. So, since physics is familiar with these classic arguments, the problem is acceleration is absolute. Not position, not velocity necessarily, but at least acceleration is absolute. So Newton had his famous bucket experiment. In the first situation, nothing is rotating, neither the bucket nor the water inside the bucket, and the water surface is flat. Later, when you set everything in rotation, the bucket is rotating along with the water at the same angular velocity, so the bucket and the water are at rest relative to one another.

7:30 But a Machian positivist can be perfectly happy doing that. All he is seeking is an economical summary of observable facts as we see them. So that's Mach-like. But of course, for most of us, we're more interested in Mach-heavy. So let's have us a new theory, please. And like Leibniz, what's the new theory we're looking for to look like? Well, we're going to assume... The relations on which dynamics should be founded are instantaneous distance relations and relative velocities and accelerations between material bodies. A partial catalogue of a relation is the acceptable quantities that we can use in dynamics. We'll assume the Euclidean structure of space now understood as the entire set of spatial relations. And of course we're assuming absolute silence and aid. Of course, writing in the 1870s or 1880s, not to have assumed the Euclidean structure of space a priori, but actually suggested a replacement for Newton's first law, but not one that had... A literal reference to the fixed frame of the stars, but something that he said is going to work out to be exactly the same thing. So Mach said that instead of the first law saying that a body which is not subject to external forces has zero acceleration relative to absolute space, we'll say that it has this quantity. It basically says that your acceleration relative to a weighted sum of the distances of all the rest of the body in the world.

10:00 The further away an object is, you might start playing with it if you're going to work out Mach 10 in its paradise. Well, relationists are meant to reject absolute space structures. Isn't the assumption of the Euclidean structure of space a bit of absolutism? I think the answer is, unfortunately, yes. In 1615, when Newton was alive, the Machian relationist century worked with Barber and Bertani,

12:30 We have two theories to look at from Herb Rattati. The first one gives you a Machian relational Lagrangian and pulls out a relationist acceptable gravitation theory from that, and I copied down these equations from all these papers from the United States. Now the first relational theory from Herb Rattati, several times, and certain nice features. You get brain dragging type effects out of this theory. So Mock's bucket does what Mock suggested it might do, as I understand it. But also, undesired, based on the way we understand observational evidence to date, objects don't display anisotropic effect. We have inertia from the galactic center that takes normal anisotropic effect for a body's inertia. Some people think that the Barber and Bertani 2 dynamics is a nicer relations theory in classical setting. Barber calls this intrinsic particle dynamics and the leading idea is that we replace inertial frames by a best matching procedure in instantaneous configurations. Think of a configuration of all the bodies in space given by the relative distances and consider a different configuration.

15:00 ...and to represent the world at a different time. He's about, with respect to it, until you minimize the intrinsic difference between the variation of the... And we recover, because of Newtonian gravitational physics, that's not a cost, it's a benefit. Because it makes a prediction of the theory something that we actually...

17:30 Imagine two globes of water, now this is adapting an example from Albert Einstein. We have globes of water, which take a spherical shape because of... And they're separated by a large distance. Well, they're separated by some distance, and they're relatively rotating. Well, the theory gets rid of absolute rotation for you. Implement Mach's ideas on the Euler's ratio.

20:00 Harvard-Ricotti 2 theory is an elegant and mathematized version of Mach light. And that's good. It's an improvement over the Newtonian mechanics. You have to stop there, but not fully satisfying if you're intrigued by the... We're going to talk about Mach's principle, again a three-space based approach, but now the approach that Wheeler tried to outline in his Geometric Dynamics. I don't know how to say that, is it Geometer Dynamics? Geometric Dynamics. Geometric Dynamics. So, Wheeler's fond of this slogan, mass energy there determines inertia here. These are the four-dimensional Einstein equations, and Wheeler wants to work out his understanding of mass-energy there, determines inertia here, using the initial value formula for Wheeler. Give the distribution of mass-energy, then solve Einstein's second-order equation for the geometry? No. Give the fields that generate mass-energy and their time rates of change? No. And give the three geometry of space and its time rate of change all at one time and solve for the four geometry of spacetime at that one time? Yes. And only then let one's equations for geometry dynamics and field dynamics go on to predict for all time the inertial structure and symmetrical structure of the world. That's the schematic description of the program. How does it work out? Here's the 1973 summary. I'm not going to put up... Any instances of the various different actions and things, because there are many different ways of trying to work out this problem, depending on what sort of initial value data you'd like to start with.

22:30 The summary of the approach to Mach's principle that they get out of the initial value formalism is going to be a 12-step. Well, you'll see the numbers 1 to 6 get repeated on the next slide. I'll be able to figure out how to change the numbering. Let's just go through the idea. So, specify everywhere the distribution and flow of mass-energy, and thereby determine the inertial properties of every test particle everywhere at all times. Sounds nice. And they say this demands first a way of speaking about everywhere, a space-like hyper-surface. Let's insist, in conformity with Einstein, that it be a closed, free geometry, and for convenience, that tau be a dependent position. Actually, I'm not sure if tau is the trace of the curvature or if it doesn't play a good role in the criticisms of the technique. Specify the three-geometry, the three-space internal metric, to the extent of giving the conformal metric. Without the specification of at least this much geometry, there would be no evident way to say where the mass energy is to be loaded. We'll come back to this conformal idea later. And now there's a step six in this. It's a very, very long, almost half a page. It's a huge book. So what it is, is an apology for what Wheeler says the next thing we have to do, which is introduce, include gravitational field stress energy. Recognize that giving the mass energy only to fields other than gravity is an inadequate way to specify the distribution of mass energy throughout space. I've deleted a third of a page. It's a big argument for why you have to count the energy included in gravity waves and binding energy and so on.

25:00 To me it's deeply suspicious of anyone. But to specify this mass, one must give enough information to characterize completely the gravitational waves on the simultaneous sigma. For this, it is not enough merely to have given the two wave coordinates per space point that one possesses in the free geometry. The two wave momenta for spacepoints appear in York's momentum density, weight, and at the same time as an extricable part of this operation, one must specify the density of flow of field energy. Then we solve for the conformal factor. We get back a real geometry. Then one has complete initial value data that satisfy the initial value equations of general relativity. And these being known, then I sense the properties of every test part are determined everywhere and at all times. Atiyah is perfectly at least compact. What's going on in that 12-step program? Here's the way I read the... In the standard initial value formulation of relativity, you specify the three geometry on a space slice and the time derivative or the extrinsic curvature or blah blah blah. There's various different kinds of tensorial quantities that you can specify on this three surface. To get your initial value stuff. And then finally, the mass-energy distribution and its flow rate of change of the three-space metric with the expinter and cell lock-locker. His tantamount does define the inertial structure that everyone is, after all, giving information about what time-like lines are straight as you depart. Supposed to be what the Machian matter distribution entails, not something that we encode as part of the initial Machian distribution.

27:30 He uses the same initial value of geometry as he can out of the true Machian distribution, I'm afraid that's not much, and then in that long quote that I omitted, he's trying to argue with you that the rest of what we need is really okay, part of the Machian initial configuration, because it's part of the job of describing gravitational mass energy. Is this really Mach's idea? Now, it's bad enough from the Machian point of view that this whole program can be done with empty space, with no material stress energy, and it can. Witten and I, that shows that what you're really doing is a description of how tree space evolves over time. That's the kind of self-centribalism, but now self-centribalism about tree spaces. Now you might debate this problem slightly by insisting that there is some matter. Wheeler seems to do that. Wheeler doesn't like to talk about working out this formulation of Mach's principle of initial value, zero matter anywhere. So you might just stipulate that there has to be some matter, and you might even decide to stipulate that there's matter everywhere, that the stress of energy is non-zero at all points of space. It seems to me that doesn't fix the real problem. The local inertial structure is being, to a significant extent, presupposed in your initial data that you're giving at the dynamic goal. I could be wrong about this, but this is my reading of these quantities that you have to assume over and above the 3D geometry. Simply an innocent specification of gravitational field stress energy, but they are rather strongly related to the inertial structure of space time, which is what you're trying to derive. So my diagnosis of the problems here is that Wheeler aims at codifying Mach's principle, but only really succeeds in codifying determinism. Give me all this initial stuff and I can tell you the future and the past evolution of what the whole space time looks like. That's determinism.

30:00 If you think about Mach's idea for the origin of inertia, let's go back to Mach's idea. Mach just said, you tell me where all the other bodies are located around right now, and how they're moving relative to me, and I'll tell you what syndrome, etc., type forces I feel. There could be other forces that are indeterministically acting on it as well. Mechanism is not Machianism. So let me set aside Wheeler's program for the moment. We'll see if it gets repeated to a large degree. Here I'm just reminding you of the Barber-Bricotti 2 Particle Dynamics Actions and just focus on these bits so that you can see the similarity between this and the fields here in a conversion event, dynamics on superspace, a procedure that Barber likes to work with now for implementing his ideas. Think of the entire class of possible Riemannian three geometries on, let's say, a compact manifold. That is Riemannian... what do you call it again? Geometry. The entire configuration space of possible Riemannian geometries. Geometry is not metric, so you want to quotient by the dichromorphism. Then when you quotient by the dichromorphism invariance, as you should, what's left is the configuration space called superspace.

32:30 And that's where Hopper wants to work out his dynamics, and so he completed that with a nice choice. Okay, so now let's go back, just take a look at these quantities, and then we go back. It's easy to see the similarity here, right? d, dx1, d-lambda is a kind of a momentum, right? And these are sort of shift terms to work out the best matching. H is the symbol we're using here for the three-space metric, and these are often called momenta, time rate of changes of the three-space metric, and n, the vector n is called the shift vector, which is shifting the three-space geometry around. Minimizing the action is accomplished by shifting the adjacent three spaces around until you get the best matching between them. And Barber's idea is that we reconceptualize general relativity as a theory about histories of relational configurations. For Barber, three-space, three-space slice, or a now, what general relativity is is a theory about the evolution of natural objects, i.e. about trajectories through this. Here, why Barber concludes that GR is mocked. Only global relative three-dimensional configurations count time do not feature the kinematical foundations of the theory. Rather, they are determined dynamically by a generalized best-matching, localized version.

35:00 Should they lapse and shift together? I don't think you can use the lapse. The lapse can be replaced. If you notice here, there's a little semicolon. It's hard to read that. That semicolon is... Now let me go on and try to make as much trouble as I can for this view and see. I'm happy to take corrections if this is, say, not right. But I have worries about whether the local inertial structure is really 100% derived and is part of the procedure rather than presupposed. And my worry is around the derivatives of the three-space metric that are playing a crucial role. D, H, I, J, lambda, or is that sort of presupposing a bit of something like a little regression structure? I guess I have a similar worry. If I understand right, this semicolon is the ordinary four-dimensional metric. No, it's not. This is a three-dimensional metric. So, but I'm still concerned about the Gruner's three-space metric being relationally innocent. And I'm still, therefore, concerned about whether we're really keeping given a Machian determination of inertia or just determinism. Of course, I agree with Oliver that stepping back a moment from the details of the dynamics, what this is, is a theory about the evolution of three elements.

37:30 Barber explicitly says, for convenience, let's suppose there's no matter anywhere. Let's suppose that no matter anywhere you're stepping quite far away from the Machian project as Einstein. This one has to do, of course, with the way that you're free to slice up four-dimensional configurations into different kinds of sheets. So you might have a dimensional general world and you have these kinds of slices. And a superspace is a bunch of intrinsic three geometries. It's a configuration space of intrinsic three geometries. And so, if the geometry of your spacetime is dynamic at all, there's a different free geometry on these various slices. And the whole general relativistic world represents a certain trajectory through the superspace. Here we've got superspace. But now, of course, you're free in general relativity to instead start like this, and then start making new ones.

40:00 Your slice is a bit different, as long as they never go time-like anywhere. You can slice up the manifold into different kinds of slices, and that would represent the trajectory that goes, you know, like this, through the superspace. And what Oliver's pointing out is that, observationally, both of these trajectories through superspace just are the same four-dimensional world. There's no observational difference between them. There are three spaces. Then it's erratically indeterminacy. Alright, so... That's not right. It's much better for Julian, but it's probably the right guy. Then that's a bit of a problem with the official book. The official book. I'm okay. I'm okay with it. I thought I had done it before without it. What all he talks about in the second of his two papers is that you can move to conformal super space and remove its degeneracy.

42:30 It seems to me that what's conformal in superspace is the geometries now are not simply quotient with respect to the amorphisms but also with respect to the conformal structure to identify any two, three geometries which are informally the same metric and that brings back the determinism in the conformal superspace. But to my way of thinking, it also destroys the last tiny shred of Machianism that was there to be found. And this is a problem that I said we'd come back to in the Wheeler 12-step program. The perspective of the idea of Machian initial data. Would you want to start with a conformal 3-geometry? Conformal geometry allows you to specify at a given point what's the density of matter there. But if you take two bits of matter in a row, a bit here and a bit there, it doesn't let you say how far apart they are. And that's totally bizarre from the perspective of the Machian idea that we started out with in particle physics. It's clarifying to me what I think we started thinking about with starting with formal geometries. But to my mind, it sort of shows that you're getting quite far away from it. Can the three-space approach that Barbara is charting here be safe? If we think about it, if we fix up Harvard's three-space machinism to bring it back more to the original idea, I think you could demand not just that there be some matter, like Wheeler seemed to do, but really that there be matter everywhere in the manifold, in the three manifolds. If you do that, then the H-I-J or the three metric that we start with becomes relationally innocent and pure. Why? Because in the process of specifying what bits of matter and what distance relations to what other bits of matter, you're going to be essentially grabbing hold of every point of space and giving the entire metrical structure that connects all the points into three space.

45:00 That still doesn't get rid of the degrees of freedom of the gravitational field. Right. It's still there, so I don't see why that's any more or less likely. So this is just to purify the three metric, but now you also have to get rid of these gravitational degrees of freedom. The only way I can see that you could try to do that would be to try to replace the three metric and its derivatives to the extent that it appears in the action with quantities that are built out of relationally acceptable stuff. I feel a departure from the spirit of most textbook developments of the initial value formalism. Normally you can't do this kind of replacement, but if we're helping ourselves to a spatial closure, if we're helping ourselves... To there being non-trivial mass-energy content at every point in space, then, I don't know, maybe it's possible to rewrite the actions of the appropriately launch in a way that only except for one. Even if this worked, however, if we're sort of fixing up the barber and co-workers' recent approach, we've still got that indeterminism in the super space. We're being inevitably driven back to a four-dimensional perspective, because you can't really claim that what really exists in our world are three-dimensional configurations, not even three-dimensional configurations of matter fields. You have this indeterminism, which reflects the rather arbitrariness and general relativity of how you slice up. What you have to really get back to is, no, these different trajectories through super space. Correspond to one physical world in its four-dimensional world.

47:30 It would be no surprise if general relativity resists being driven away from the four-dimensional perspective. So let's re-examine a four-dimensional approach to Mach's principles. Ideas, when he responded to Newton's bucket, seemed to call for a three-space approach. But can we rehabilitate relationism without that? Well, as I said before, the core idea of relationism is to deny absolute space. This is actually how Einstein first wrote the Fox Principle in 1918 and his response to Kretschmann. Not quite a perfect remaining quote, but very close. It can be satisfied by Fiat, who just insists that the completely empty space finds an unphysical solution. Why not do that? Well, of course, a lot of the most interesting solutions for mathematicians and even physicists are indeed empty spaces. And yet, at the same time, there's a distinguished history in physics. Ruling out certain classes of solutions on the basis of having things you don't like, like non-zero cosmological constant or singularities, negative energies and so on. So it's an interesting possibility to consider, just ruling out spacetimes with no material stress energy at all. But B remains to be done, and B is of course very problematic. It's vague and fuzzy. But I want to insist on the importance, as Aldi did, of the fact that general relativity is different from other theories in not having any background absolute structure.

50:00 Many of the models that should be most troubling from the perspective of Machian relationism, like Schwarzschild geometry or Vosky geometry, in many of these objectionable models you can see exactly how quasi-absoluteness All of this arises despite the promising beginning of having no background, because you're imposing conditions of flatness at infinity. Not structural. It comes out of the, you don't use boundaries. It comes out of the star of a symmetry. So I can teach you, don't use boundaries. So spherical symmetry plus what else? Because Friedman, you know, this is mysterious. Static, well, empty space, I think. Zero right hand side. But still, it seems to me that you can at least say that when a model has matter located in an isolated region, and then, that's not Machiavelli. And so we might just think about, directly enforced in the force-based approach, tackling again the question, how can we rule out models of general relativity that display these kinds of non-Machiavelli conditions? It will involve these kind of restrictions on the model class that have to be justified by an argument that such restrictions as you put on the model class entail a satisfaction of B. But I'm afraid I can't get you beyond the vague fuzzy.

52:30 Can I ask about the constraint with the values? The way I put it is that Bohr is right that you can take both. Think about the very simplest formalisms for the initial value of a treatment. What do you specify? You have to have the metric on the 3-space and the extrinsic curvature. And the extrinsic curvature tensor is telling you how the 3-space is embedded in the 4-space. So it's telling you, essentially, how this 3-space relates to the immediately adjacent. It's essentially telling you something about what the affine connection is going to look like. And I don't think it's completely the same as giving the affine connection in the region. I think it's so closely related that it's a bit suspicious from the perspective of the project. In Sandwich you specify the two surfaces and then you have a lapse and a shift that allows you to calculate what fills the Sandwich.

55:00 But my worry is that there's a bit more than meets the eye going on in the action, like the shift function. Presuppose anything at all that's four-dimensional. Well, I didn't really understand the distinction between the two. Just on the bar one, you seem to say that the fact that you have time derivatives, but those time derivatives are just neutrally and don't really move around the foundation of time. Well, lambda is not... It's not proper time or anything like that. That's right. At the same time, does that mean that they're automatically, in no way, encoding part of the international structure? If you're right, I'm actually happier. I was making these criticisms, but it would be nice if I could believe that. So from the perspective of Eugene Barber's view, were you happy to have his ontology be primarily an ontology of three spaces?

57:30 I don't think they're problematic. What I would like to see then is to try to get the same quantities now out of the rivers with respect to lambda material stuff. One is, when you start with a 3D manifold, do you assume that topology is given? They do, they assume it. Shouldn't topology also be given a manifold? In fact, let me point out the results. I just found out that Bernardo Law has been working on Feynman-type quantization, and she has discovered that the dimension of the four-dimensional manifold now becomes a technical variable. There's a class which is four dimensions, but there are solutions with other fractional dimensions, for example. In my point of view, where I regard the inertial gravitational field as the inherently gravitational conditions that make the coronal geometry go along with the gravitational field, there is no general relativity, there's no such thing. It just depends on the inertial gravitational field you're already in. By me, I meant to use to mean... Yes, but I mean, if you mean, geometry and mathematics seem to be in a lot of trouble from the point of view of quantum graphics. People have shown that, you know, there's an alternative representation, just as you could take...

1:00:00 And they find that there's a Hilbert space representation only for the kinematic mechanisms that literally does not make sense. There's a unique representation for these. And he's throwing their results, but there it is. I mean, there's value in context, though, which is certainly implied here. The last one, unless you make some, you specify the last one, it should be one. It's a parallel to the other, so it's a bit to get into the problem, though. On the last point, about this question, can you eliminate the field? Mathematical microscopy shows in the slow-motion parts, but in the post-post-post-post-post-post-post-post-post-post-post-post-post-post-post-

1:02:30 It seems to be a contradiction. He wants to run a relationist program for him to say, well, let's start with the idea that there's nothing there. To me, too. That's quite an attitude. But I said there is not. It is not the case that there is nothing there. It's inertial gravitational field. Why is that worse than a lot of math? It's not the kind of thing that serves as a source on the right-hand side of the equation. It's not material in that sense. It's a generator of gravity. So even if you have gravitational waves, something bare, you can think of just a simple bare manifold with nothing, and then you can think of one with a robust matrix. The latter is a richer structure. There's something more there. What would you say about the Kruskal metaphor? If you look at it from far away, any text will say that mass is there, but when you go in and emerge, there's no place where you say, ah, there's where the mass is, so does it or does it not? Does it or does it not have mass? So the metric allowance of the behavior of the mass, how do you get it?

1:05:00 Good results go in the opposite direction in trying to get the materials produced to make Hawking happen in general. So the answer to this question is, why does Julian Saber consider these type of... When I've asked him that, he says something similar to John's response, which is that you have to think of, say, the energy and gravity waves as real stuff. So it doesn't count. The matrix and its degrees of freedom as part of the material stuff I saw, I just, for my purposes, is cashing out box ideas to think more old-fashioned perspective and see what can happen. Does that mean he's automatically denying his relations to the cosmology of mathematics? It's getting quite unclear there. He gets a bit more relations than he's going to be. Well, remember I had this mistaken understanding of absolutism. But if you have that mistaken understanding of absolutism, then Julian is definitely a relationist to the core, because he always insists on a different orgasm. It's not that I'm intrigued with him. You get afforded it, but most of the time it's a variance coming out of a piece. He's a relationist in that sense of not starting from the surface of the planet. I have something to ask you about the work you're working on with EDM. How does it best fit the model of this entity? Why should there always be an opinion that you need the best of them? The best matching. But why does the best matching cost us always a value factor? Why can't we at all? If you start with configurations that are really, the way to think about it is,

1:07:30 configurations that are rather only slightly different from one another, plus shift rotations, whatever you want. Since Hollywood, what would you say about it? Yeah, same thing. So, we've got some functions, which function as masses and relatives of the tree. There's a change in distance of 0.49. And if you're considering finite distances of dimensions, you're kidding if you're going to put it in a migration space. I think that you probably do need a finite number of particles and a finite maximum separation if you allow things to go to the infinity of dimensions. I was just going to make a comment on the informal, my view of the informal field of this case. There's, just considering the particle, Julian generalises the initial goals of the theory to include global scale. And from a relational point of view, that seems to make sense, because I think in general relations, there's no absolute certainty of the first level of science. All those. There aren't absolute facts about relative distances. There's only the fact that the universe is treated equally in the past because there's, you know, twice as much distance as that. So, when you eat global quantum transformations in a faster way, that does seem to be a genuine thing in relation to physics. The irony, as you say, is that when you go to the general relative of the analog,

1:10:00 I mean, the conformal theory isn't actually, in general relativity, contrasted to the true geodesic principle of Hawking space. It's actually a geodesic principle of a conformal, a configuration space that you get when you're doing conformal, local conformal transformations. But then what do you result in? So it's exactly the opposite. You know, the thing that you should make sure is that this is a global volume. I think it might be, you know, that's why this distance exists. Actually, this is what I didn't quite understand that. It sounded like you said the relation is, rather than trying to get double the distance, then the relation comes in between the two words. But why is that relation? I mean, the relation, I thought, was the idea, it's basically the relation between various cultures. That's what I meant. Now, if you look at the five-order organization itself, the relations are five meters apart. Six meters apart. Only if you've got at least the four relations in mind, such as the base relations are congruent, twice as long. So if you're a relationship, it's really... That's what relationship in particular is one way of fleshing out the version of a relationship. In response to a question you might have about the original, I would use it to say that it's just a logical fact that this thing has a five-meter relation to this thing. But why do you think that's in better standing than congruence or choice of form? I don't understand that. But you can raise a question. I was asking you about the operational meaning, the distances introduced. If we imagine ourselves sort of inserted into the two globes' world, well, there would be a factor value standing next to one of those, how big the other one looks. Things like that, I guess. I have a question about the globe that's going to have your Mark-Heavy, Mark-Light thing.

1:12:30 Does it sound like what you're saying about both of the totality being Mark-Light, that in order to be Mark-Heavy one has to have some sort of causal notion of mass distribution causing inertial structure? And that's not clear to me that cause is an appropriate notion. To use in this sort of setting. And it wasn't clear to me when you introduced the distinction between mark-wise and mark-heavy, the mark-heavier that you just said, oh, we need a new theory here, which doesn't appeal to, you know, civic structures or whatever, we just need a new theory. It's not clear to me if that new theory can actually be one in which there's, you can't see formation of cause, why can't there just be a theory in which... It turns out that you can't derive the emotional structure from the data that Lauren was talking about. That makes a lot of sense, although I didn't use the word cause. I was giving it that kind of strong view. And you're right, you're from the globes world. I've got my relational dynamics as far as perfectly relational quantities. What more do you really need to get rid of that sort of space? The original mathematical idea is the same as the form of positivism if you just look out and see things and talk about how things change and expect these things you see. The Bo and the Totti thing isn't positivist in that sense. It's just saying the world is going fixed. It's not like that in the sense that it just captures a fragment and satisfies class later. Thank you for your attention.

1:15:00 What I meant to do is contrast that with the Farber-Vertagli one had a problem that it predicts anisotropic inertia and that is very, very difficult part as well. During the table, the Farber-Vertagli two doesn't predict frame dragging, but we all hope to see it in the GR2 program. I think there was one part where you were worried about the Euclidean structure. My idea was that Newton, say, faced with Harvard or Tate too. Well, you say that there's no absolute space. How come it's a restriction on your models? It doesn't flow out of your dynamics laws to throw a restriction on pre-oriented models that the distance relations are embeddable equally in geometry. That's because we live in absolute space. Whether that's a good thing to say, I'm not sure, but... It sounds quite unlikely. Boots used to make an act of acceleration, and there appeared to be an asymmetry which the relations couldn't predict. They could just postulate if that's a right angle and this is two people in the lab and that's two five people in the lab. They could postulate this as being two different relations. And then as a dialectic, your idea would be to leave that to the students. And you would be able to derive that. Whereas they've got to take this as something through to the students. The idea is it's got to be nice and explanatory to you rather than somehow unable to do justice to you. But is it, again, is it not the case that even when you look at who clearly lapsed in space, there's always a more effective way to have many, many points, which then more or less, primitively, have certain relationship points? Distance relations between points themselves is not obviously getting explained in terms of anything deeply.

1:17:30 I think a little bit more structurally, I don't think, I would like to say, here's a structure on a certain point. Be a realist about it. It's a piece of furniture just like this. Is that a good explanation? It explains why, when they are located in space, have the distance relations embeddable in each living structure. Which we are embedded in absolute space, and it has that structure. Right, but if we're trying to just expand it, if we're trying to go from one theory to the other, if we're looking at the overall explanatory power of the two theories, If the number of things that you postulate until you get an explanation are equal to the number of derivatives and relations, then they are all there and it isn't really an explanation. I can explain why the chair is red. You'd think it's a primitive, but then you've got the expansion in the form of the expression, so there's explanation of the problem if you can get that out, but the worry is that it's not really a step forward if the variable of the theory takes as many new primitives as the dominance of the group is, and actually it turns out to be the same. Although there's explanation there, it's not clear to me how long it's better off than these relations. It's not that the overall theory is really simple. Does that mean that a relationist can just reject the question, why are you this incredible and brilliant structure and not some other structure?

1:20:00 You could say we all have primitives, and the primitives that you've got here seem to be as complicated. That's not clear to me. That was a discussion I was going to say. I guess I'm so infected with the general optimistic perspective. Because it really is variable. There's a lot to be something that you can go and explain. Well, you've not, this is not on the wide globe hidden bar. You never mentioned the tiny view about time as an illusion. Could you explain what he means by that and what you think about it? Between barbers? Yeah. No, I heard him give a talk on this when he was introducing his book, The End of Time. I understand it in the case of the classical theory. It's just that you don't presuppose an absolute time. Metric, you derive it out of the, I think I understand that way, and in essence, time is not absolute, time is real, for God's sake, and in a barbaric, funny world, the only thing real is, I can't begin to explain the barbarous quantum-related fields like that. Can I just say that, can I just say that time doesn't exist, it's a massive misnomer, it's just book-selling stuff, it's not actually real. It's a good book of mine. You can find the book and read it, but the time is long just isn't really how I should be describing what he's saying. He's saying time should go and stand with us. We might do a little bit of Mary Baker, Eddie and Christian science. Pain doesn't exist. And Mark Flynn wanted to know if that's so. Why did they both howl? Right, and on that note, howling dogs. Let's thank Karl and the rest of the audience. Thank you very much.