Background Independence in Quantum Gravity / Left & Right in Mathematics

0:00 So you were on the case. At the other extreme, you could go to some sort of account like Armstrong, that the metaphysical modality is to be cashed out in terms of some sort of relations between universals, and then you presumably, we were talking about this just before we went down, would have some sort of account of the instantiation of those universals which would avoid objects, not objects in the physicist's sense, of course, but objects in the metaphysical sense, as, you know, that which has properties or that which sort of instantiate universals. Yeah, and there would... Yeah. Because, you know, when you were saying, well, look, it's just a matter of language, we've grown up with this language that Socrates is mortal, subject-predicate languages. We can just as easily talk about mortality Socrates. Someone might say, well, can we just as easily? Because that has all sorts of implications, not only for the logic and language, but for the kind of metaphysics we have. And so if you're going to do that, appropriate metaphysics of modality that gives you all you want, gives you, say, an Armstrongian picture, but without instantiators that satisfy those criteria of Humean supervenience and so on. Answers on a postcard. What was the question? The question is, where do you see, where would you put yourself in that view? Because someone like, I don't know if this is unfair, maybe Anjan would say something like, modality has to do with, in a sense, the powers that objects have, causal powers and so on. And those causal powers are going to some way be situated, located on, or associated with objects, whether you go to Cartwright and think of these objects as having inherent causal powers or whether you talk about dispositions or whatever. And that's presumably the sort of message that you want to avoid. Yeah. Okay.

2:30 Well, look, I think what I've tried to argue is for a certain minimal commitment. Right. Now, whether or not you can then go beyond that minimal commitment to give some fuller account of what underlies that. So suppose you think you understand what I mean by and then you want to do some more metaphysics to explain what underlies that, then it could be properties of universal, or it could be dispositionalism, dispositions all the way down or something. I mean, I'd sort of say, well, it depends. I'm not going to be neutral about those. You can't be completely neutral, though, can you? In advance of seeing someone give a particular version, which I can then, like, assess. So, why can't I be neutral at this stage about that? Because you can't be neutral about anything that ultimately is going to involve metaphysical objects. Right, but my reasons for rejecting that are going to be just reasons that give rise to motivation for structuralism in the first place. So, I mean, any view that suggests that science is converging on an account of some fundamental set of objects, I would say is just falsified by the history. now I mean the advantage of the way of looking at it that I have is that it makes it possible for you to understand that the thought that there might be no end to the scientific enterprise that even physics might just go on forever that whenever you think even whenever you get to some physical theory there will always be some further structural analysis possible? I guess my worry is if structural realism is committed to a radical new metaphysics modality the non-structural realism is going to say that's a price too high. Hold on, but why is it a radical new metaphysics? All it is is saying... Well, can you appropriate... Say someone says, look, Armstrong works for me. Can you appropriate chunks of the Armstrong account?

5:00 and make it acceptable to a structural realist. If you can do that, then it's a cheap option. If it's not, it might become too expensive. OK, so what's wrong with Armstrong? Well, the problem that Armstrong's got is he's got to explain what the connections between universals have to do with the connections between particulars. That is, you have these necessary connections between universals but they are somehow abstracts and then you want to know what's that got to do with this particular array being f And Armstrong's ontology as a whole has a whole bunch of other commitments I want to avoid, like the strong truth-maker principle, and commitment to their being, you know, he's the latest account, he's got a commitment to their being a super-fact, and sort of myriology about facts, so that, Yeah, because the strongest true paper principle means that there has to be something in the world that makes it true that there are no unicorns. So then you have the problem with, like, you don't want to say it's a negative fact that makes it true that there are no unicorns. So the only thing I can do is say, well, there is a fact which is a combination, a neurological combination of all the facts that there are. And then that fact's failure to include unicorns as part of it is what makes it true that there are no unicorns. But it just seems to me to be a sort of baroque metaphysical construction that's sort of unmotivated and particularly, I mean the particular universal, I mean just the classic problems with universal instantiation relation. you know, you want to know well look, you told me that you universal theorists say that wherever there's a relation there must be a universal and then a particular instantiates the universal particulars instantiate the universal, but now the relation between particulars and universals seems to itself, I mean that instantiation is itself a relation

7:30 so now there's going to be some universal of instantiation you've got this regress set in, right? So I just sort of think that there's a load of sort of problems in that picture of universes that sort of make me aware of that. Whether or not it's strictly incompatible with structural realism, probably not. I mean, when Manchester interjected that all of a problem with Armstrong is he makes no connection with real physics. It would still be universal. And we'd like to see how this fits into physics. We never chose that. We never know how to follow him in history. I mean, maybe we'll be abandoned and flesh it out with physics. He seems to deliberately set it up in opposition to the extent of mathematics and physics. And that's the only important part. I mean, it's quite ironic, actually, that Van Thrasen is the big anti-realist, yeah, whenever you've got to get into a, I mean, you see Van Thrasen in a debate with a realist metaphysician, and it's really ironic, Van Thrasen has much more concern for the science. and you know I mean recently there was Van Inwagen a classic example of a realist and metaposition and Van Frassen side by side at his reading conference and Van Inwagen was drawing his ontology on the board you know it's got these categories and Van Frassen at one point says well do you care what science tells us the world's like and Van Inwagen says oh yeah of course a tidied up version of my ontology will fit whatever science comes along in the future and then you just saying, well, why, especially given that your ontology has, and often you have, individuals, right, and that, you know, it just seems, it's sort of totally disingenuous, and the next physical position of the Funderland-Ivanian one is entirely motivated by his understanding, his understanding of science as it was, sort of, a hundred years ago, or two hundred years ago, or something, so he puts up this ontology which is really motivated, the only reason you would have thought of it is because of science, the only reason you would say that the fundamental particles is because of science, But then he then sort of professes lack of concern with what current science says about that. And you think you can't look at both of those.

10:00 You either say, I'm just going to do complete a priori of mental physics, but then if you're doing that, why on earth? You'd think, well, fundamental particles have an issue, I don't know. Or you're doing something that's motivated by science, in which case you ought to go as far as you can in looking at what science actually says, rather than just stopping any sort of naive, inherited view of what science says. The point about physics is if there are those problems, once you have physics, then they become of much greater interest. in a sense they become detached from physics I'm interested in them whereas detached from physics these bloody problems you're thinking well those are telling us that this framework is a mistake so who's confident about that on behalf of my metaphysician colleagues they would say well bloody well get on with it then I mean you're complaining our metaphysics isn't any good so why you guys aren't coming up with an appropriate metaphysics not only for physics but for your understanding is it? And then their response is well, well, it's hard. But we are. They are and it is. But, I mean, they tend to reject any account that doesn't fit in with their conception of what mental physics is as not counting as mental physics. That's a decisive problem. I mean, the thing about the universe is it's basically a account of resentment, but then as it turns out, because Brookings Armstrong is a sparse theory to that universe, he doesn't think there's a universal corresponding to every predicate. So then it turns out that things like green don't count as proper universals, but then you've lost sight of them. Well, whatever story you're going to have to tell about resemblance for green things isn't going to be a story in terms of universals, and now I've lost sight of the motivation of thinking I needed universals to give an account of resemblance anyway, because it turns out you know, it gets bang on all this stuff about universals motivated by talking about things sharing properties in the ordinary sense, and then it turns out that we have the only universalist that likes to speak and charge and, you know, something out there and spatio-temporal ones or something and then you're like, well, okay so, it's not going to be universals that do the work in explaining and of course he's going to say

12:30 well, actually, ultimately green things get to be green in virtue of sharing these more fundamental, but there's no of a story that we can tell about that, right? There's no, it doesn't seem to be, it doesn't seem that we can ground out resemblances that we identify at one level of description in terms of fundamental physics. I mean, it's not even clear to me that you can recover atomic bonding from fundamental physics unless you make assumptions which are only motivated, you know, and assumptions are only motivated when you know where you're going. You can show that physics and chemistry are compatible and in some sense you can make the bridge between the two. But if you started with quantum mechanics and no one told you anything else, you'd never deduce the existence of atomic structure. Well, no, I think it's pretty good. No, no. Is that this? Yeah. It's a hand-on-in-law. From a physical point of view, it's the same. Quantum theory, the quantum amaxio, it's the quantum of the atomic structure for a physicist. Because you discover it there. Right, but you, of course, but when you proceed, if you write down the abstract theory of quantum mechanics, Unless you make certain idealizations which are entirely unmotivated at just the pure level of quantum physics, you can't get back on to chemistry. So it's only by making assumptions that are motivated by chemistry that you can recover chemistry from physics. I understand, but mathematics is not physics. To put the question in this way, the conversation is off. If you are in a physics of chemistry departments, you look at things in a certain way. If you are in a mathematical department, you start with Hilbert Spaces and Mathematics. Yeah, okay. There are two different parts of looking at the reality. Yeah, sure. I'd just like to put in one very brief writer on behalf of Armstrong, although I completely agree that his metaphysics of universals

15:00 is set up in opposition to current physics and certainly doesn't attempt to make contact with it, he does attempt to make contact with mathematics and he does have this quite elaborate account of the natural numbers, the reals, and even of the complex numbers in terms of main-run structural universals. I don't think it works, but he does at least make some attempt to show how it would connect up with basic mathematical structures. that's just it well I'm very happy to introduce Dean Rickles who's a PhD student of ours at the University of Leeds co-organiser of the 12 Foundations of Physics conference which we're hosting at Leeds in September and there's still Still time and still room to register and participate. Only £50, it's a bargain. He's one of the contributors to the book edited by Catherine and Eleanor on symmetries in physics. He was instrumental in getting a workshop together for the Fossil Science Association last year on structuralism and quantum gravity that featured Lee Smolin, John Baez and John Stachel. And that workshop has led to a collection of papers on structuralist approaches to quantum gravity, which hopefully will be coming out in Oxford University Press next year. And he's going to be talking today about background independence and quantum gravity, yet more grist for the structural realist mill. Question? Yeah, I was originally going to do this talk just on background independence, and what I was going to try to show was that it was structurally as principle, because it got rid of absolute objects, which I take to be very non-structural things, because they're very long relationship with time, so I'm taking it to be structurally in that sense. And the quantum aspect was really incidentalised, I don't know how that played a role in the types of quantum gravity theory that they get to be designed. And then it kind of builds up the problems that arise from the background of it. But when I finished that paper I realised that a slightly stronger push towards structural realism in particular could be that if we use the quantum aspect as well,

17:30 background and dependence aspect. And this is what I'm going to talk about today instead. So to show the quantitative theory pushes towards a strong structural position, and not only does it push towards a structural position, it pushes away, it moves away from So I should begin by saying what I mean by background structure, background dependence, background dependence, and then I'd say a little bit about how quantum field theory is background dependent, and whether background dependence manifests itself in quantum field theory, or whether it's a necessary feature of quantum theory and background structure. Then I will say a bit about the background of independence and general relativity, and how that management itself, and what kind of problems that leads to, especially to do with the real authenticity of that theory. Then we want to discuss quantum gravity and which I would say to be bringing and trying to merge background-dependent theory with background-independent theory, or trying to get background-independent theory. And finally, I did a few arguments, and I think, an argument that put it towards structural realism, based on much, much, much deeper as well from the Okay, so there are a variety of ways to characterize that and probably philosophers will know this as an absolute object or an aggregate element in a Latin instance, or an absolute object with freedom or in Anderson, and you can find that very freedom in Anderson today. And it's basically to be contrasted with dynamic, or to absolute contrast with dynamic, or to absolute contrast with relational qualities. The reason why I choose to use background structure is, well firstly, absolute is a slightly slippery concept.

20:00 Freedom is in which is free senses, but absolute in the space that day we call it. But then I realize the background structure is actually quite slippery as well. It's not exactly as easy to define it. So we can do a few possible definitions. So the first one that you might see is an object that doesn't obey reaction-reaction principle. How you affect the physical content of the theory, but it won't be affected itself by that physical content. Or we can say that it's an object, this is the mathematical version of the most often seen in physics, an object that appears in the Lagrangian theory, but isn't buried along with the other variables I think that's the definition of an agent. And then we have another definition. The background structure is an object that's invariant of models of the theory. So, and we can give an example of such a structure. Probably the best, most obvious examples of theories which contain background structures are space-time theories, where we can factor the theory, the overall space-time structure into various background structures such as the metric, the connection, the outlying structure of the topology, the differential structure, and even the continuum of the bottom there. I think most of the losses when we say background structure are referring to just the metric So, as an example, we give a maxwellian electrodynamics, which have a Lagrangian, which involves the cost of energy, the regimented, across the space. And this, of course, plays a role as a vital role in the equation of motion and dynamic, potential it could not be a possible projection that confideration is based. And the fields themselves are time-dependent functions, so it requires a cost-load rate of . But what we find is that when we solve the equations we don't have the metric, the metrics stay the same throughout the procedure. So for example, if I were to turn the lights which are in here, it would give a different solution or a metric itself will not have changed.

22:30 They do the same with the likes of each and the likes of each. So, I prefer the model theoretic definition, it's more than the endodges, the values, the molecules of, so it's been said that any assignment of values to the variables of the theory is the metric of the models. The metric will be fixed across the dynamics and models of the theory. The background structure creates simply models fixed across the dynamics and models of the theory. And then we can simply define background-dependent and background-independence as various possessing background-dependent structures that are going to be background-dependent, and background-independence is simply defined as freedom of background-structures. So background-structures are mistaken. So I'm sure there are countering those ones, but there's actually another thing I wanted to say about that. I mean, an essential part is that the background structure is causally connected with the biblical concept of the theory. It actually does play a role in the term in the background of the theory. You can't just sit there and work with the background structure in a theory that just is there for no part of reason. The one that just alters throughout the models for no part of reason. So we need some kind of correlation between background structure and background structure. I'll give an example where the way from here is independent of the product of it. I guess that means it's not a way to actually manage it. So one thing we notice about background-independence is that we distinguish various levels of background-independence. So I mentioned that as a philosopher, as a particular treatment centre of background independence, as being suddenly restricted to the metric of the spectrum. But in actual fact, as a precision kind of shows in all of the results, we can fact-rate in many different ways,

25:00 and find the whole spectrum differential, the manifold point of view, and we don't have to observe those kind of background spectrums, as we observe it. So, we basically, I won't be explaining how much background attendance should our theories have. So, with our high air, normal air seems to suggest that we should do it to the level where we still talk about physics and do equations and do physics. It's kind of problematic, but, um, slowly it's a bit more radical, I thought we should just abolish all possible backgrounds, I guess. In which it's how to see how you can do, I don't think like that, how to see how you can do to draw any backgrounds, especially, you know, how we define it above. So I think I'd be fair to say that we should apply our background independence to the level of physics. The general philosophy suggests that we should be background independent to the level of metric, so that's where we should apply our background. Unless it suggests that. We have to go beyond that and explain something. And what we find is that at the level of the metric and the decon, quantum theory can come higher to construct, but that's just the problem of quantum gravity. And structural positions tend to be less quantitative. Originally I thought that was, I was just going to talk about background independence, but when we learn the two, when we think of quantum theories but we find the structure of the positions where it is especially bottom-up and I would say substance-highway positions and relationship positions were very, very about the spot. Okay, so why is that important to create a back-hand penalty? Or where do I have that to start? Well, firstly, I want to know physically important theories are background-dependent. They require fixed metrics. So in the Gal-Laney-Berry cases, The system is all in respect to absolute time provider, and they are invariable to become

27:30 an angel of the nations. Any of the allies in the nations of the Gail-Aing group is given to our physically reasonable properties of the theory. So clearly the metrics entering there in an essential way, we have time, we have space which is given. So, we have two questions then. First, where does this structure enter into quantum theories? Secondly, is that necessary? Can we do quantum theories without that structure? I think the first question first. Well, clearly there are numerous areas where the penance comes out of this itself. You think of the operators in quantum theory, which in part you can find that instance of time, and also get even time-commitential relations. Sequences given yet by lots of panel operators to get that, and it almost becomes a component of the cosmic structure that's given by the time column to give it a fixed metric. Can I just ask, this is a lot of freedom about what exactly is to be included in the metric? Um, well I was trying to sign it a little bit, but, um, we're talking about some sort of contact at work, um, you may want to, you may or may not, um, include the masses in the metric, but you may or may... Well, okay, I mean, we're not restricted to one single type of metric, that's not the issue of choice, Well, why is it going to be fixed in these areas? You can't bury it. Well, it depends on... do you mean fixed over what? Space or fixed over...? Fixed over time, it's not a... Well, fixed over time. What kind of constraints do you do? I wouldn't have... So, for instance, the metric may include information of constraints,

30:00 and the constraints are buried in time. Certainly, in class, it would be a new one. In every quantum theory, in every physical quantum theory, the metric will not be able to come into a state of state. There's no back reaction, and so what you have to do is decide what metric you want to work with, and then you go and you set up your quantum theory and you work out your quantum theory, but you don't have a way of feeding that back into the Einstein equations to tell you how the metric is going to... But the models he's talking about, right? I mean, you're helping him just. I'm not sure. That's why I feel they're in her space, right? It's still fake. It's a gentleman. Right. It's still fake. Well, sure. I'm talking about a lot of those situations. But there's a little book by . One, Tencils and Planets and Astrosby, which basically the class of the canon, he talks about, I'm sure he had played it as well, and he certainly talks about constraints in one canon as well, and, well I can't remember if he talks about time-dependent constraints in one canon. Do you think that in these cases the metric at one time will be different to the metric at another time, and this is state-dependent? No, not state-dependent, I'm just saying that, well my first statement was simply that what is to be included and what is not included in the metric is the automatic taste. So the metric can contain an awful lot. In fact, if you have a more general notion of what the metric is, and we're talking about the five of the four. Do you know what I mean about the five of the genre? The first operation builds into the genre transformation here when you differentiate with, when you have a restriction of the logarithm with respect to the tan space. And you talk differentially. OK. Right, OK, yeah. So we're finding a period sharing of the structure of the operators.

32:30 What else do we find now? And we also find it in the configuration space, which you find and we were actually given in terms of Newton's and of course anyone else to consider it. Probably the most well-known region where the background of men, and of course there is the Wanda-Cosalian Division, which is one of the white brands for the Axel Apple. And I think the background metric and the background structure fits into it somewhere, generally through to the Poincare group, but it's in there in all of them, not because we're getting Poincare group, the asymmetries, but we're in constant space. Okay, so micro-quartology conditions say that basically space-time separated from fields or building a space-like separate from the support between the smeared fields, or space-like separate from the region, even dealing with the outbreak, to satisfy a commutation of the past. Basically, the legends made in one point of space-time can't affect the legends made in a space-like separation. We also come back to the structure and entering the other level of interpretation. I know Steve Weinstein has mentioned this before. The best way of characterising a classical observer is to use a timeline like her, basically. This is only a classical thing, it's often derived from a classical space-time, so even at that level of interpretation we'll be using that as an interpretation. So there's a lot more for everybody else as well. So is that dependence necessary for the local part? Is the dependence necessary, but yes it is for It's not necessarily a good model or relational theories, so we can construct certain models like climate and climate and field theories, which don't have this depend on the problems or we can have relational theories, where we have a complete relational space, as well as instances, and the natural principle of this space.

35:00 And this is what we have, that we generate our dynamics from that below. And I think that this is a tiny merge, one step as well, or is it an absolute time? And the Bible puts out to you. It may just be a classic. Right. There's no point for that one. So it has to be one more type of for the value. Depending to the point two, it was only the problem of evolution because according to me one of the main properties of the fixed matrix is that it is deciding the causal structure of space time the matrix is carrying two informations one is the causal structure of space time and the second one are the simultaneity surface, which are the Cauchy surface for the field equations, both at the classical and the quantum level, and which ensure the dictability of the equation. So, in some sense, the main information given by the fixed method is just, not only the causality, but the simultaneity surface, the Cauchy surface. That is fixed once for all because we are at the absolute time. The problem of spatial relativity is that you need a team in which the evolution is in some sense the same in whichever single pushing surface issues. And this usually is not an infantile suffrage, because otherwise you cannot formulate it, because you are not aware of it, but you must be aware of it. And you must be aware of it. So this independence between space-like times is not very important. It is going to be formulated on every space-like surface and then to see which is the information you can't start, because this separation will change in the surface, in the surface you choose, genetically.

37:30 This is the problem of the communication of clocks, you cannot make measurements before you are synchronized, only clocks on a state like Star. But I didn't know that you're talking about speciality. Yeah, but every time you have a Minkowski metric, as I have a grammar metric, also one in theory is the general problem. The logic is first you have to synchronize it with blocks, and then you start to do something. So next, the background in the independence of general relativity. So we're probably used to a whole argument which is basically a result of background independence, or it arises from background independence to general relativity. And this basically boils down to the fact that the metric is dynamical in general relativity because it's replaced with gravitational fields, but we don't have a metric, and we have a gravitational field, we'll replace the rule of the metric, which would be in the gravitational field as well. So we don't have to possess a metric on that, and we might, of course, say it possesses independence at a level of global technology, because we have to solve the global technology as well, but not the global technology. So the definition is that it's, where we have the curvature of metric columns, and that is treated by the Einstein equations. And after breaking the script, I decided that these equations are generally invariant, which is just to say that if you have a model by a manifold, a metric tensor and a stress-energy tensor, then you can get one, an equivalent model, by pushing forward the metric as well. This is generally used for the owner that the substantial distribution is to ease the owner, because if the points of the original metric are to infinity identity, then we must have a distinct model in the other case, in the Diffie-Rawker case,

40:00 they're going to represent the shuffles around the points. So we can't predict what's going to happen because we don't know which one will rig and which one will mimic it. We can get that color by the vacuum of the Einstein equations in a very different orbit of the monocle. It's a black circuit of the monocle. And you want to map points around the monocle rather than using a different core on the system to look at the same things. And the same way you look at the geopsis, is there a background in the independence in the atmosphere? Well, because background independence in the business system is basically just a geometric dynamic rather than a background structure. The geometric is no longer a background structure. So what are the consequences of the fact when we reduce the general relativity? Well, first of all, the energy interventive effects are affected by the metric from the So we can say that metric is no longer a background structure for GR, and GR is a background independent. Other consequences, we have to solve simultaneous of the math distribution and metric on space-time. Points of medical lack physical content due to the variables in the variance. It's just a random point. Physical quantity, we find to be those that are individual models and variants, that are independent of the choice of all of those. And the main point is that localization becomes a relation of individual models and variants, that we're no longer able to localize the points or the original model, because the points really don't have any physical significance, prior to giving a solution. So generally, these consequences are being used as part of our items, being used as part of our relationship, and there's also a lot of structuralism, with Stachel and Gerarder as well.

42:30 But given these properties, combined with false nature, I think there's also a strong support of structuralism, and that's the aim of the other two positions. So firstly, before we go on to that, what's quantum gravity? I can give a little definition. I think this is one of Sam's constraints. Is this Sam or Cal? Okay, and this is one of Sam's main constraints in the region paper. And that's just that constant gravity is a theory with the two limits, G goes to zero, pi's constant goes to zero, to the pi's group, GR, I might have a physical perspective. And we generally find, well, there are a variety of ways of distinguishing the types of approaches, but fagron, bagron, dependence and intelligence is one way of dividing the approaches. So examples of bagron-dependent approaches are, for instance, to the original co-variant approaches. A lot of student theory, for example, background-dependent theory, is not one part of the ideal theory or theory of use. But we find that most of these types of approaches, background-dependent approaches, have failed to be consistent approaches, generally to get through normal ability problems, especially in the co-variant approach. And let's just generally explain this, having to do with the fact that we can localize points and consider regions of integration in that place. And that's where the equations tend to work. Another thing, I've got a top point, is that these properties tend to be quite more structural, more relational, in points of a priori in-line by a fixed-metric template. Localization is absolutely applied to define a priori fixed-metric template. The background-dependent theories tend to be more evolutionary. We now have a look at the gravity and the field theories, which are intended for background-metric and background-metric, in terms of differential structures, respectively. The counter-problems will meet in these, of course, tend to be more conceptual. There are loads of philosophical discussion of them, but they tend to be couched in the process. And we also find that distinctly structural, relational, points are not anecdotally,

45:00 where I can individuate, but I think that we find that localisation is relativised, because it has the individual origin carriers. Excuse me, what way do you see conceptualized about the root of a new character? Because there is a problem of conceptual problems of general relativity. So it's a kind of problem with conceptual problems in general that feed into the problems of the back of the important structures, like the whole object, which describes the problem of time, and from the observable. So, in a sense, the drawback from quantum gravity is that it's not being that hot space in that you don't know how good particle it is. It's a string theory as particle it is. But it is the only example, so we have on the market, of a background independent theory, in which the role of the gravitational field is asymmetrical with respect to the other fields. Because the magnetism teaches to the other fields the causal structure. In extreme theory, the graviton, the photon, the gluon are all the same frame. This information is completely lost. Unfortunately, in quantum gravity, you don't know the default on this stage, but non-sexual is the first attempt to have the gravity on a different, non-sexual level, with respect to the other part. Because the metric tensor is carrying the chrono-geometric transformation as a dynamic transformation. So it is the magic text of it, from St. Mancombe, which teaches to the other things, which is because of the structure of the space-time. This information is completely lost in thinking. Thank you very much. The other point is that if you go to the end of the structure point of view, and you put together the Bergman-Kommer point of view, at the end of the day, the space-time is the gravitation object set. a problem of localization and design form, which is a kind of structural So the gravitation of field is the space-time and teaches the how the structure to the other fields. This is the message of the

47:30 background-independent fields. We don't have examples in which we where both gravity and particles. String theory hopes to arrive at the end of the earth. Martin is not changing the picture, to my understanding. He's only providing resources for the mission of gravity and the other forces. But if you follow the line of structure, for example, everything is in a different way, when you have to identify the points of space-time with matter. But if you put together a structure at Berman, you arrive at the conclusion that the points are individuated by the gravitation of these itself. So in some sense, space-time gravitation of things are the same. And that's kind of what I'm saying as well, and that's quite structured to pretend. Because once you quantize the gravitation of things, then it's hard to think about the space-time points as well. That's the open point. Because hashtags are already a small thing, bypassing the problem of quantizing on video on. And you look at the space-time vision. Because if you quantize the metric, you lose the causal structure. You don't know what the space like and time like. So they avoid this problem quantize theology. But unfortunately they get a non-force space, so you lose the intuition. But where does the causal structure mean to that? I mean, can you just give you a lecture? I mean, this is magical. To my understanding, no one is able to solve the problem of the causal structure and quantum gravity at this stage. Because string theory has to be the ground structure, so it has no problem. But all the other approaches, if you quantize a default factor, you are lost. You don't know, you lose all the concepts that are all the causal. You do not define the space-like distance, the time-like intervals and so on. I mean, that's precisely why they are sort of conscious.

50:00 In quantum gravity, you have a, you lose the space-time, you get an abstract structure. And then you try to, their problem is how to recover a co-screening of this structure which make contact with general gravity. So the problem is shifted to the co-screening. If you are a human, you'll come up to that kind of company now, which is one of the speculators of incest. And this is kind of what we discussed. How do we exhibit background independent theory? If there's incest theory, the background is, the physically relevant quantity is going That doesn't necessarily have to put you into more structures, for example, if you are relational. But where do we add the quantum theoretic aspect? If you're going to have a relational, you need to have results that are going to be able to individuate the points of space-time. How can you do this in which you've got classical objects with well-defined properties? Substantially, we'll use the points of space-time which I'm going to take to be classical and extended to individuate physical objects and their properties. So in this kind of context where we've got a relational theory and we have quantized properties as well, quantized objects as well, what sense can be made of a version of an object and a version of an entity in this context? It doesn't say that we can go relational, because we haven't got any decent objects, any lollified objects. We can't go to a certain level, because we haven't got a lollified space standpoint. So what is the way out of this? How do we feel to the points and the objects individuated? Well, I mean, that's how I see structuralism arising.

52:30 Besides, from that kind of paradigm, we can go to some type of paradigm, we can go to structural. And that's kind of it. I think maybe that's the question of the two aspects, but just because we kind of have a relational aspect of the timelines. I do have a comment. Here, the real problem is that we do not have a background independent theory of measurement of the classical theory. So you are putting all these problems at the quantum level and you don't have the answer to these problems at the classical level. Because the only existing human measurements in general relativity is done with test objects. And test objects are dependent on the actual reaction that's not told. So we are still able to develop a consistent So you need to say one more time, but it needs to be back out in the end of the first place. To most physicists, it comes to the side, you certainly need to know that you've got a couple of arguments that you want back out in the first place. And back in the end of the season seem to be failing. Even the string pairs are needed to try and start to get back out in the first place. Now you have to give me 12 experiments in the solar system, all around the solar system, with a very high level of precision to the light of clocks, which have a system's level of decision, you have to test all the non-graphic ideas, one of the six-two or one of the six-four. You have to start to learn the rules of the game and the automatic theory of management. When you don't understand this level, all the speculations at the upper level are open. You don't have a classical background

55:00 Well, I was going to sort of ask following on from that, because one of the criticisms that Simon raises against Sauer's book is that he just dismisses the measurement problem. Now, is that a general problem for any kind of structuralism? Is there preferred solutions to it that strike one as meshing with some kind of structuralist understanding of either quantum theory, quantum field theory, or quantum gravity? The question is, it's really to do with measurement. Is measurement a problem for the structuralist? If it isn't, are there preferred solutions to the measurement problem that strike one's particularly structuralism-oriented? I mean, at this stage, approach but you know if you've got a solution because this question was raised up in what do we mean by maybe one can understand you've got a structuralist account of quantum gravity and then someone might say ah but yeah but look wait a minute what what do we mean by a moment we've got an observer bang we've got something non-structural coming in I guess one of them comes from the effort, which may be worth it, I don't know. Can I just add a bit? Yeah. I think absolutely, that structuralism sets constraints on the satisfactory solution for measurement problem. Speaking to Baz about this recently, his point of view is, look, if the issue is, to give an account of physics in terms of categorical properties, the probability of this is what sets the problem. and that's exactly the feature of the Everest interpretation that it interprets probability in terms of categorical problems and then it's the only approach to test that. So it's slightly more general it's not just measuring the problem and how to solve it, but how to deal with probability I think, I have no idea what in many ways Lewis attempts to deal with probability in terms of categorical properties, and he seems that's very challenging but I do think that the given framework does provide a solution for that, which is a structural solution. Maybe there's a similar approach that does the same, I don't know. And a pilot big theory is, sure, it's kind of dark, but in general that probably means it's just an idea.

57:30 And it has the same lack of clarity that probably you guys understand, that's what it does on the canvas. I don't know what it is. Physicists typically don't see that as well. I was saying I'm prepared to run the other one. Can I sit down? Can I sit down? I have another question just to make it clear is it the case then that relationism is ruled out because we can have a relationist account of general relativity you've still got classical objects. So once you have quantum theory, then you're going to have problems. It's a relationship. It's hard to see how those objects can then individuate space-type points, as people like Durand have seen . There seems to need a classical gravitational field to individuate the point. But isn't that just going to be the measurement problem, again, in the quantum gravitational sense that we're going to have to have some sort of .. So, for example, if you had some sort of collapse I don't know where you get the notion of time, but every so often you just collapse down to some classical solution, right? Well, then you're going to have your classical space-time, you're going to be able to individuate things, etc. Or if you take some sort of invariable approach, you're going to have to say, well, look, in that case, there really is some sort of ontological thing there that can serve as the underlying relations that I'm interested in, but I just don't happen to know what they are because they're hidden from me for some reason or something along those lines. Say it again? It doesn't go away, it's all that, and it's all that. The generic problem why you don't have material measurements is that you don't have enough

1:00:00 solution of Einstein equations to the matter. No intelligent solution will matter with which build dynamical objects to make the measurements and not test objects. This is the real problem. You don't control the matter side of the Einstein There are beautiful solutions with black holes and so on, but if you have to build a clock as an oscillator inside general relativity, you are able to do it. We're going to have a similar problem with one field theory if we try to perform measurements too. We're going to have to analyze what does it mean to have a complete state, and this is why we always resort to having some sort of box-based scattering and then we can make sense of these things, but if we wanted to talk about the state of the universe and the quantum field theory conceptually, that's highly problematic. Yeah, it's conceptually difficult. You are asking much less. The only attempt I know is by David in which he tried to put a theory on measurements with small deviation of weak gravitational fields. Sure. I guess the question is just, back to Dean, is it really, is the relationalist really in trouble here? I mean, we might even want to try to save the subtitle list if we want it to be difficult. So you're saying, well look, the relationalist is in trouble because you don't have this, the relationalist needs classical objects, right? And I take it, and I'm sort of wondering about, well, do we really need classical objects in order to be relationships? Why can't we have relations between non-classical objects, or why can't we have non-classical relationships? I mean, after all, once we have quantum mechanics, we've got fuzzy properties, presumably we have fuzzy relations. Why can't I, why does this push me all the way towards something like structuralism? Is it just the case that my relationalism isn't going to look like we're being used to impress in the classical way? That's just a question. It's a view I want to defend. Yeah, but it's cool. Given these kind of relations, how do you cook? How are these relations supposed to integrate? Well, it's hard to know, but then I wonder whether it's hard to know just because we don't have

1:02:30 the theory and understand the theory, right? On the other hand, it does seem that I don't want to undermine, because I'm actually supporting it with you, but couldn't one say, well, a relationist might say, okay, I'm going to start with some sort of fuzzy quantum object, and that's going to give me, the relations between those fuzzy objects are going to give me fuzzy spaces or places in a space. So I might not get points, but I can get something from... I mean, I can get something in a sense that some people have said that Newton had before he was thinking... Well, Koslow, I think, has this historical paper where he says what Newton was actually thinking about, this is in response to some grooming stuff, isn't infinitesimal points, but actually little places. And one can stitch that together in an appropriate way to get you what you need. I think one needs to be fairly clear and robust about how relationism gets ruled out. I mean you could go the French ladyman line and say well it gets ruled out because we just don't have any notion of an object because of the metaphysical undetermination okay that's boring and Simon disagrees with it so as soon as you do that then you need to come up with an alternative argument that's going to decisively rule because it seems the relations could sneak back. I haven't considered it all. It does seem tied to an interpretation as well. I have a simple question. I didn't understand how structurism is distinguished in relationism. Well, the structurism And as I say, it's a slightly different duality in terms of pictures and pictures. When you have those two objects, you can't find an object properly, you know it's very simple to look at the objects, but then that's a problem, you can't find them. They've got a larger density than the individual. I might mind that sort of view of the microscopic level, and of course the problem of relation is going to prevent this and has to recover like the starting structures so at some level we have to recover the structures

1:05:00 so is the difference that structurism doesn't have an ocean logic present at some bottom level whereas relationism does albeit it's a relation of the structure This is the fact that the hearing is completely out of control. There is something to cover space time that we could use in the Bible again. Thank you. Here I was talking about that. I am telling you that this perhaps close the page is in my mind. One often takes for granted that when one uses the term equal for common, the concept associated to this term should be a plus type of logic. But this is not a necessary assumption. We might refer to the notion of an individual that does not behave as a kind of logical individual, a kind of logical individual, a notion of an individual that is not generally able to decide scientifically over the process. And so perhaps only general discussion about structuralism should refer also to this possibility. First of all, change the logic in our basic notion of human people. So, but would that still have to be invituated with these kind of, you know, or still using the English as a quality of these to be invituated? Now I shall have a few of them, and I shall have that sort of. We should refer to the general logical theory where individuals have other properties with respect to the standard classical property.

1:07:30 For instance, we might refer to what set theory and these kind of things. So first of all, weaken your logical framework, not refer to classical semantics, this is too strong in many aspects. Your self-theory might be a quasi-theory, your logic, your predicate logic might be not a standard classical predicate logic, a kind of a first-order quantum logic or first-order false logic. and so all the discussion is different if you refer to the weaker logical framework I mean I agree with that however it is enormously difficult just to go if you begin with class set theory or quasi set theory or some non-standard set theory and then try to get try to recover fox space for example we tested Krauss and I sort of made moves along that way say look, in quantum field theory if you really think like Paul Teller that there are these non-individual quanta then you can't really represent quantum field theory in terms of the semantic approach or model-threatic approach you really should be writing it in a form of quasi-set theory but boy, I mean that was a real struggle to see how it comes out that's one way to go, but one would need to even think how to do it in, say, quantum gravity in that format. It would be quite a conceptual difficult problem. The difficulty is represented by the fact that your mathematics loses classical logic. So your notion of mathematical point is a classical notion from the logical point of view. So one should this weaker logic with classical logic that after all is necessary to use the mathematics you are using in this framework you have every kind of logic but it is possible to solve coexistence

1:10:00 of different logics in one and the same field Sure. Question, not to be interested in the discussion, but if you want to characterize background independence in terms of first condition and action, well, in that case, if the background So the background being fixed would presumably be a sufficient condition, but not necessary. So I'm saying that we can have a very low background to play on our phone without... Coaching with that. Yeah, that's sort of related to what I was saying before. Yeah. But that wouldn't, I don't, I suppose what we should have in terms of a routine of an object, which interacts with other things but isn't interacting with others. So we can't just sit there and change for no reason. And that change needs to escape. Yeah, yeah, but I mean, I understand that we should escape that changes, that changes, well not random, but due to something in rather kind of circumstances. Now, they're changing the sports and circumstances which can't bear them. It's not going to be bad at the time. Thank you. Any other comments? A comment that would be interesting. What is really lacking is that here are the macroscopic points, in general, the classical methods we found here. And here the obstacle, why not to try to point masses, like the spatial relativity, is that you get mass divergences which no one is able to renormalize. So there is something deep connected with the mass which is there. Because again, if you go to the quantum theory of measurements, which exists only in the non-relativistic framework in the given environment, there you learn that to make a good measurement, your object must become a heavier.

1:12:30 Now, since in general relativity you have only test objects to do, due to these masses, here you get a contradiction, because to make sense of the material elements of performance being microscopically heavy, but if they became heavy, there are no more test masses, but But they influence the gravitation on things. And here you have a vicious circle which has to be broken somewhere. So, behind all the problems of quantum gravity, whatever it means, you have these basic problems which are completely ununderstood. And the masses, the less understood aspect of the particle in general. It's the first one ahead of all. And here, the mass is a very heavy load in this circle. So I have the idea of trying to clarify this point. We are looking at the semi-classical theory of microscopic objects. Do you have a reference, right? It's the first one ahead of all. There is practically nothing. Everyone has received a formalization of this problem, as usual, even under pirata. There is no one who knows how to adapt that. Thank you. Thank you very much. Well, as for the title, I think this is

1:15:00 I should be proving the distance of fish, I think, is my title. This has been up to my title, as your current theme. Perhaps another title would be the generalist picture. This is a term due to the writing of Hawthorne and Cover in their recent book on Leibniz. The equivalent term would be semantic universalism, that's Bassett and Rasmussen's term for it. It's, I think, a form of realism that has a long and horrible tradition. It goes back to Leibniz and to the pre-critical card. is rejecting the generalist picture, and I think that's probably as good a way of understanding what the critical term amounted to would become. I think it got lost so much in the 19th century, but in Russell's study on lay fits. The batting time got rather lost with the subsequent movement and logical positivism. I think Karnat had sympathies with this, but there it took again a slightly different turn in terms of the kind of higher order structuralism. The empiricists had little to say about the logical empiricists later on. With the 60s, scientific realism and so on, it never figured. And I hope there has been more interesting in the last ten years, and it's now going to be an interest in it. Okay, so I'll give a couple of examples of present-day interest in it. But just at this point, perhaps, let me say what I'm going to talk about. A bit about how identity figures in the general... I should say this part. The generalist picture is, in the cruise terms, the view that purely qualitative descriptions are adequate to physics. And, of course, we have to say what qualitative descriptions amount to.

1:17:30 I suppose the key idea is that indexicals, demonstratives, playing their own role, are not even. Okay, so I'll say a bit about how identity comes in here, and why a principle of identity in the symbols might be needed. In both a minute, being aligned with the principle of identity in the symbols, one needs to know what the real predicates are, or the predicates that are physically meaningful. And this is where symmetry plays a particularly important role. I think we can understand this in terms of norms versus initial conditions, that what thought to be required of norms is also required of additional conditions. And then I want to say a bit about mathematics and how math and statistical physics. Okay, now, this gentleman's picture, I think, could be the whole of my talk, because actually it links most directly with the themes from this morning. But I did want to talk about discrete signatures, and in particular reversions social reversions and come back to Kant and how that figured in history for work and how presently a problem that I think the challenge to the generalist picture is really posed by parity and charge conjugation symmetry violation I've put it in space and time here only because if one was to account of the generalist picture that there should be in there and play a very important role. I want to say something very briefly about space because it feeds through a possible solution to parity validation and how to understand. I think I understand my talk up to here, but I think here I probably lose control of my subject I'll do my best Yes, but it is a little bit difficult to do it without reading text, and I don't want to read text. Even reading text probably needs to be complicated. I do hope to be intentional up until this final point. it's an example of how generalism I think does and has cropped up

1:20:00 with major effect in modern philosophy here I have an extra inquiring pursuit of truth and constitutional relativity not in the sense of learning how the scholar problems do arise in moral theory but just in terms of that arise in set theory, and of course model theory is very largely giving a set theoretic model of formal syntax. So this is about, you know, there's a rabbit. Are we talking about cosmic complements of rabbits or are we talking about the rabbit? At what point was proxy functions whereby you commute the objects of reference? This was also behind Putman's worries about moral theory. In Putman's 1977 APA address, Lennon and Sperman creeps in, likewise in the Pines article was logical and volatility. But both of these writers eventually just settled for the very simple, actually, non-categorical theory in the logical and pathological sense, where you do have, every model is asomorphic. But the fact that you can form these permutations creates a real worry both for Putnam. And I think one of the worries is Quine, actually, is some sort of vindication for Quine of his positions about what's going to go as a reference. And these words continue to inform Putnam right out until the present time. And another example is in Basta. I think it's only a problem that comes up when you get to the present. You don't have to be able to address any sort of problem figures. But here's Bas talking about a problem acute for any approach to science which characterizes physical theory primarily in terms of mathematical models. And we have to characterize, we have to use mathematical models in probability of science. That's what I'm going to say. and he's saying here that any mathematical description is unique and most like to isomorphism, given attached labels but attaching also has a literal sense only existence of some function which is in turn subject to the same limitations of description well, Bass has got a variety of warrants here and the sort of permutation arguments running in the Kupfer case and the Kine case are not the only ones

1:22:30 he's also worried about standard difficulties making sense of reference purely predicated terms let me put some stuff on the left I can not say that so some of Bass's worries to typical counterexamples to identity of indescribables, and whether the principle of identity of indescribables can be defended. I'm talking about a generalist picture that's usually associated with identity of indescribables, maybe that one can only talk about journalism a la Lange, in surprise what does such a principle. And then the typical counter-examples are blacks, two spheres of ions, space, one of my parts, exactly like, or Strausson's checkboard, and you have a symmetric arrangement of chess pieces, and one can't make identifying reference to any one of them, and this and Strausson's work is supposed to show the insensibility of what equals an indexable or a demonstrative component of thought, identifying thought. But I hope all of this is familiar and I can quickly go on. Is anybody very possible with what I've just said? So, these are legendary counter examples, but I think are not very good ones. and they're not very good in the light of Fregean logic. And it seems to me that in accepting that relations are perfectly personal predicates, as we all do in S. Frege, and as almost nobody did in S. Frege, masters have simply been rather sloppy about how Frege is the principle of identity and sound. So to be phrased in terms of objects, to be distinct objects, must differ in terms of someone and property, or in terms of their relations. That's supposed to be a rough statement from a principle of identity with symbols that allows relations. And then in the case of Max Wap's two spheres of man, they have the same relations, which spheres satisfies the same relations, therefore they are not distinct, but they clearly are.

1:25:00 So that seems to be the argument. and what one needs to be annoying is that in saying that x equals y if known as well, the quantifier of the creditors but suppose one has a plan and it has no creditors and fx if known as fy and this is for all f called f1, f2, and so on, and there's a finite list of predicates. What people have been rather savvy about is they need to appreciate that there may be other free variables in the predicates left here, and in particular one can quantify over them, so that one's got statements like this, that x equals y if you can only get from all z, fzx if you can only get fzy, and likewise all z and x are muted, and z for all z from darwin, which is now three-place predicate in conjunctions and permutations. So we've got all these conditions to worry about here only if all of these are satisfied, the one can identify x and y. And then one notices that in the case of that's two spheres of iron, of course, any, and what one has there, and what clearly does the neighbor wants to discern the two spheres of iron, is that there is a credit, which is false. The credit is one mile apart. a two-case statement so f is x 1 mile apart from z well, so it's not the case for all z, this is the case when z is x the value of x and d one sphere is not 1 mile apart itself although y is 1 mile apart from x so for that value of z, this will be false, hence this will be false So there's a history here, this goes back to the book of the Nice of 1912 or so, it follows Goebbels' extremitisation of identity in order to improve the frequency of the catalyst.

1:27:30 It was taken up by Quine, but Quine did not illustrate it and, in fact, miss an important category of dissenters where there is such a probability that the sort I just indicated, which is a symmetric vector. Quine did notice that you could discern objects by an asymmetric relationship. And this example was of a directed line where the points are discernible by virtue of satisfying a non-symmetric primary relationship. Joseph was relatively discernible as opposed to absolutely discernible, I noticed that the weakly discernment case, in which they are actually satisfied with an irreflexive symmetry correlation, and that's the one that covers most of the philosophical, the counterexamples are familiar in the philosophical literature. Okay, so going back on identity, in this analysis of identity I claim covers every So in other words, no classical camera example to this principle of identity. In quantum mechanics there are camera examples to this principle of identity, but we can turn them around and use this principle to deduce that indeed Indeed, those objects should not be calculus objects, the common example is bosons, elementary bosons, for which there is no predicate that I have really been able to formulate, by which they can even be weakly discerned. So the suggestion now is that indeed we should not consider elementary bosons to be objects. We should consider the objects, in this case, to the modes of the quantum field, which take our different magnitudes, the magnitudes of integral value, and we mistakenly think that those integral value magnitudes give us a number of objects, and that's just a mistake. So that would be the view. Thirdly honest, we're always really discernible, so this is actually a conservative sense of objects in the quantum domain equally as it has to. Okay, so all of that on the side of the gentleman's picture and in favour of it. And I just want to note that I don't really think that there's anything wrong with identity. I don't, myself, see why would you insist that identity must be analysed in terms of credulence.

1:30:00 I think identity is perfectly clear. I think set theory with its dependence on an anonymized whose way it is satisfactory, there is no conceptual difficulty somehow there so, and indeed there's nothing wrong with using not equal to x not equal to y as indeed a symmetric irreflexive privilege by which we discern the two things And I think that the generalist fiction would work perfectly well using the identity sign in an analysed way. And the point of the generalist fiction is I think just conceptual transparency. We know exactly what we're talking about. There is nothing okay to the mind in this sense. So why bother with an analysis of identity? Well, for me, at least, the point of an analysis of identity is just that physics works with mathematics not with a formalized language, nor with set theory. And at the level of the mathematics used in physics, we do not see the identity sign in the logical sense. So how can we understand the mathematical physics that we have, so as to understand identity and non-magneticity of options? We didn't have a defined object at all. And it seems to me that what is much easier to arrive at from physics, in the language in which it's actually discovered and thought about, mainly mathematics and all of its programming, It seems to me that we learn better how to write down predicates corresponding to physical magnitudes than anything else. And that's partly a function of the fact that we, in terms of experiment, we measure magnitudes. And the magnitude is a short step to arriving at predicates. I think we also have every theory is born with an interpretation of rough and ready to this we have some sort of rough and ready interpretation of every physical theory in terms of objects and in terms therefore

1:32:30 of some notion of identity of objects but it is rough and ready and how to make it more systematic and more precise I think we can do it better and in a more systematic and clearer way by going to a system of predicates from the physics, and then introducing the identity side in terms of the analysis I just gave, which I thought would be a nice analysis. And I'll move on to the next topic soon. This seems to work in a variety of different contexts. And I pursued it in a variety of different contexts in recent papers, and in particular for the Catherine and Ernest's recent book. Excuse me, from the university point of view, if you have many dates, you should have also subjects from the near-releasing point of view. Otherwise, we might have seen recent cases. I agree that, as I say, there is a problem interpreted. We had a rough and rainy interpretation of every physical theory. Now, I think we may make mistakes, though, in that interpretation. And so this is a project of how to, in a systematic way, go about clarifying our interpretation correcting our interpretation and the suggestion is that this analysis of identity is a way to do that in particular to make more precise what are the objects of theorem now coming on to the question of what are the real predicates I think symmetries provide us with a useful principle the general principle of whether there are exact symmetries, the real physical predicates, the quantities that are physically real, physically measurable. I don't want to tie this, though, to what is measurable as to what is observable and what is observable. So I'll just say, what are the real predicates of those that are invariant under the exact symmetries? And with that, one now can actually do the analysis in a variety of cases. So, translations, rotations, space and time, discrete symmetries, gauge symmetries, and it seems to work pretty well in every case except the one I'm going to come on to, P and C, so that's what's setting the problems of the generous picture as I see it.

1:35:00 But now, looking at this criterion I'm using of symmetry, I think that there was a general and widespread view that laws should be co-variant, not invariant, under exact symmetries. But it was okay for the initial conditions to break those symmetries. a very widespread view among physicists. And I think there's a very interesting question here as to just how physicists have understood symmetries over, especially the last 50 or so years. I've got three examples from three physicists I admire very much, all of which I think are really mistaken. So, this may be something people will feel strongly about. The first is Dirac, from his introduction to the first of every edition of the Principles of Quantum Mechanics, where he says the things we are immediately aware of are the relations of these nearly invariants, by which I think he means quantities to the principle of covariance, to a certain frame of reference, usually one chosen so as to introduce special simplifying features which are unimportant from the point of view of general theory. I just think this is wrong I think that what we are immediately aware of are invariants another example this is Niels Paul Paul comes in from an awful lot of state but I think he did magnificent things in his early life at least while the theory of relativity reminds us of the subjective character of all physical phenomena, a character which depends essentially upon the state of motion of the observer. Now this is from his first collection, I forget who Jesse was from which he called, it's the Top Theory of Humanology. Again, I think this is completely false. There's no subjective character of physical phenomena introduced by special

1:37:30 again, everything that we are aware of and observe are invariably invariably characterized objects and to give my third example this is Herman Weil I think it's the 49 translation into English, but here he talks about objective versus the objective relative versus the subjective absolute He says this objective world is of necessity relative, it can be represented by definite things, numbers or other symbols, only after a symbol of coordinates has been arbitrarily carried into the world. Again, I think this is just a mistake. Because I think everything what we're immediately aware of is what is physically real, and everything is subject to illusions, and what is physically real is what is invariant. More than only, invariant quantities and illusions are what is physically real. I agree completely with you, Simon, of course. To be fair, I always feel a little unhappy putting the vial next to Dirac and Bohr. Dirac and Bohr are fairly philosophically unreflective physicists, or in Bohr's case, sometimes quite confused. I think Bayer, even at this late stage, was still heavily influenced by certain philosophical positions that he had quite sophisticated views about. So if you read the philosophy of mathematics and natural science, the Husserlian position comes out. This is tied... So I'm just saying, I'm just saying, it's tied to this notion of the ego. If we're going to go from the ego to an objective world, we have to essentially export this system of coordinates. from Boar's rather naive phenomenon. It may well be, but I think what's important here is not so much whether they were making the same mistake as whether they were reinforcing one another in a way of talking about symmetries that I think is misleading, but false, actually. Let me take the struggle behind it. I think it's... I don't think that Dillard is naive. Sorry? I don't think that Dillard is naive.

1:40:00 Well, I'm saying it's false, not naive. No, I'm not saying he was naive as a philosopher. I'm just saying, it's a minor point, I'm just saying. No, I think it's the sense of being aware of what we are aware of. It's not in the sense of what we are. I think it's another sense. Well, that better. Maybe, but I think there's a straightforward sense of what we're aware of is what I see, and I don't want to, I say that what we see is real, and we are not subject to illusions or accusations, and what is real is what is American, so that's... Can we come back to this, because I think that the probability consensus is that maybe we can tell the world is to be strong. You might say this in a favor, but I think you've heard Weinberg say that the asymmetric distribution of galaxies in the sky is breaking rotational symmetry, which I think is absolutely false. So this is something that the physicist's assumption one bird would say we should expect there would be some debate about this. But let me leave it to the end. I mean, this is just a reminder if I want to consistently follow through and it needs to, wherever it does, it needs to follow. And you can pick apart the various assumptions I'm making if you wish at different times. Let me come back to my list. So I've talked about laws versus initial conditions, and, well, from the end, the commentator was to make, where I think there's some, the idea that the initial conditions do not have to be invariant under the symmetries. What is correct about that is that you can define initial conditions in a way that is not invariant under the symmetries, likewise the final data, but then what you'd better it's only the relation between the two that is physically meaningful. And that makes sense for the rigid symmetries. It does make sense for the local symmetries, the gauge symmetries and so on. And I think that's the real content of what physicists have been doing in using initial data as not data for varying random symmetries.

1:42:30 They've used that data, they've derived final data from it, from a covariance of equations, and then it's actually the relationship between those two sets of data that is invariant of the symmetries that is carrying the physical meaning. But if you take that initial data literally as specifying physical states of affairs at a given time, then one ought to be defining defining that data as itself invariant under all of the exact symmetries. Okay, now, just something about mathematics. This will feed into space. Let's talk about space and come back to mathematics. The great example of this use of translations and rotations of space is, of course, the Lagos Park and Charles C. Now, the point I want to make is that if space is defined as something homogeneous mesotropic from the beginning then I think Leibniz clearly saying the right thing and Clark was clearly saying the wrong thing. It's under the paper on the projector there. It's not a projector. And Clark was saying the wrong thing. And since both Clark and Newton and Leibniz all agreed that space is homogeneous and the isotropic, you know, lightness and how there is winning out. But it's not that there was any, something unintelligible about the notion that space might have had privileged positions. And the reason why that clearly is not unintelligible is because, after all, with the mathematicalists we can set up a Cartesian coordinate system where there's an origin and where we have real numbers labeling every coin. and why not use those real numbers why not use that Cartesian coordinate system in a physics I see no natural reason why not you could just have a physics where there's a special point called pi and one could insofar as the physics was empirically predictive maybe say where pi was why not and where the zero was and so on So, it's not that there's something unintelligible about breaking this translation symmetry. One can do it mathematically in thought, and one can use that in physics.

1:45:00 If you can get content in physics, then fine. That's the point I want to make here, and it's going to be very relevant to what happens with P and C. Okay, now, let me just say something very brief about time. In this generous picture, you may feel that, you know, may think it is somewhat legalistic. Why are you so bothered about the ethicals and demonstrativity and what's wrong with the damn things? I mean the kind of issue that I think arises when it comes to time is the block universe picture, so the two nations where one has the world line, and the issue is whether this is adequate, is it expressively adequate to change. So I hope this is all very familiar to you, and I just want to remind you of the kinds of problems that will arise around the endless debates that go on about it. I want to say that this is backwards to our understanding of time, but it clearly involves a fair bit of anguish. At some level, there's something deeply shocking about this view of change. And, again, I'll talk about Weill and Steve, who will be upset with me for it. Weill talks about consciousness crawling up this world line, which of course isn't any good at all. That's introducing a meta-time, and what one has to say is that consciousness is everywhere. It's everywhere on this world line. And what one further has to say is that crawling, like any other kind of emotional change, is represented by the structure of this world mind in space-time. So that goes with the generalist picture, as I understand it. And those are some of the reasons why I object to it. With some of that damage force does us say that we cannot represent ourselves. By all means we can draw such a world map, we can represent the system of motion in terms of the block universe, but we have to stand outside of it to make use of it, and of course outside of it,

1:47:30 we're not really outside of space-time, we are within space-time, and I cannot meaningfully represent myself within space-time in these terms. I have to make irreducible use of index fields and so on. Okay, so now let me go on to discrete signatures, which is what I'm really focusing on. I don't want to focus on the continuous signatures here. I want to focus on the discrete ones. The first point is, is this really important to the history of the last four? And there's a fair amount of debate about that. My claim is that it is. It was certainly important to likeness. and it was a ball to Cunt I don't know how much time to spend on this issue I'm doing quite a lot so far, aren't I? Have I found? Cunt first brought up the issue of spatial aversion how do we understand the left-right distinction in the context of the Newtonians versus the Leibnizians 1768, in the direction of the space, and here he's saying that, well, if you take the Lannitzian point of view, then all natural space is simply the space occupied by a hand, so it's right. However, there's no difference in the relation of the parts of the hand to each other, and that's so whether it be a right hand or a left hand, therefore the hand be completely determinate in respect to such property. Now that's supposed to be the problem for the Laiditia, the relational conception of space. He doesn't exactly say though how Newtonians are supposed to deal with it. This is the nearest he gets to it in his first essay. He says, our considerations make it plain that the determinations of space are are not the consequences of the positions of the parts of matter relative to each other. On the contrary, the latter are the consequences of the former. Okay, so relational positions are consequences of determinations of space. Our consideration is to make it clear that the differences and true differences of that

1:50:00 can be found in the constitution of bodies, these differences relating exclusively to up to its original space. Now what does that mean? The best account that I've come across during this end is where he talks about orienting as opposed to non-orienting spaces the idea being that in a non-orienting space there can be nothing in the object itself that makes it a left hand rather than a right hand but if it was an orienting space then there can be such a distinction distinction lies in relation to the body of space as a whole, maybe it's oriental or non-oriental. I say that's the best account of it. I don't think that's what Kant had in mind, and I don't think it really goes that far, so I think it's not actually a satisfaction. Kant's final remark in this paper is, I think, very germane to what happened next in his thinking. He says this, Finally, our considerations make the following point clear. absolute space is not an object of outer sensation. It is rather a fundamental concept which first of all makes possible all such outer sensation. For this reason, there is only one way in which we can perceive that which, in the form of a body, exclusively involves reference to pure space, and that is by holding one body against other bodies. And I don't understand the lesson at all. but why is Jermaine what comes next is because here we're starting to worry about epistemology alright, if it is something about space itself that is the ground for orientation of quality still is the question of how do we recognize the distinction and here he falls back on surely how do we recognize the distinction but now the worry is that that that basis of recognizing the distinction seems to have nothing to do with the relation of the body to the space in itself. And so I think it's a real problem at this point. And I think Kant came to the view that this was a real problem. And two years later, in the inaugural dissertation, he returns to this theme and now concludes that the issue is that there is nothing, as he says, in respect of everything expressed by means of characteristic mass intelligible to the mind through speech, there is nothing by which, well, if we only make use of those concepts intelligible to mind through speech, we cannot substitute, we would be able to substitute the left from the grave.

1:52:30 And now the claim is, well, it's not by Marx's discursive concepts intelligible to the mind of his speech. It's not through those that we recognize the distinction. It's just through perceiving the distinction, to see the things in the left hand rather than the right hand. And now the claim is that cognitions must always be treated as derived from perception here, no matter how extensive the logical use of the understanding may be in relation to them, they are called sensitive on account of their genesis, and not on account of their comparison and respect of identity or opposition. Even the most general empirical laws are nevertheless sensory, and the principles of sensitive form, which are found in geometry, no matter how much the understanding may operate on them by reasoning, nevertheless do not cease to belong to the class of the world sensitive. So he's saying that this contaminates now the whole of terminology, and thereby the whole of science. So I think we have a very clear idea here of how this problem shifted the calculatory rejection of the whole notion framework between his transcendental idealism and the view that scientific knowledge is concerned only with what is given in intuition or looked over by the understanding of all that stuff. And here he's repeating the same thing. We can apprehend concretely various directions. And here specifically this goes left and right. It's only a surprise that one of the gates of the lion and so on. And now look here, he makes the analogy in case of time, among different times, the time which is earlier and the time which is later, cannot be defined in any way by any characteristic marks, which can be conceived by the understanding of unless you are willing to involve yourself in a vicious circle. Okay, the mildly discerns the distinction between them by a singular intervention. Okay, now I bring all that up because, you know, I guess this has all got to be understood as controversial.

1:55:00 And the reason is, if you have someone, if you're a fellow of Henry Anson, who is probably the most respected Count, in any way today, a Count scholar, saying here in the column of the Gomenon, and again in the Benedictine Foundations, Count appeals to the paradox of the common counterparts in support of the transnational idealization of many other in space. No right to my knowledge does even suggest that there must be a comparable argument concerning time. Okay, this is a mortal statement from Alison. I don't have to go through the evidence, but it's very clear how exactly parallel the problem between how it can pass with the direction of time in the inaugural dissertation. It didn't in the particular reason, because the direction of time got to be so bound up with causation, and causation had to be a product of categorical thought, a product of consciousness to be human, so it didn't fit very well in the aesthetic, and so on. So I think that's how that goes. Okay, so let me let me now just give the solution becomes a paradox in accordance with the general framework that I'm, or the project as I'm presenting it as the generalist picture. In accordance with exact symmetries, the only real quantum quantities are invariant. Now if mirroring the exact symmetry, then this world as it is, as a mirror image of this world, should be one and the same. And then that seems to raise a paradox, because the hand in space and in the universe would be rather a left hand or a right hand, it seems. The mirror it would be one of the same, how can that be? And the answer is that our understanding of what is left of the self, what is right of the self, is indeed found out with relations to things that are not geometric. So, crucial things, anthropomorphic things, things like

1:57:30 the human heart, things like most people write with one hand rather than the others, the same hand, giving the term right, which pedals accelerate, which is the brake. Those are the things that characterise the right of itself as goes the left of itself. And in In the American image universe, it would remain the case that the bright pale is the one you would call bright. I think you see how this goes. To back this up, I mean this may seem wildly uncomfortable to you, but to back this up, Now, imagine that you've got the neurological image of yourself, of your brain, as you think, staring at your left hand, this is the left hand, and I recognize my left hand, so the mirror image is having very good neurological processes of producing mirror image sound waves, which say, they make noise, you know, this is a left hand that I see, okay? you've got the mirror image, neurons firing, and so on and so forth. Now, unless you believe in an arognitive theory of mind, whereby thought supervenes on neurologic processes in such a way that the mirror image neurologic processes mean the mirror image thought, something like that, then I think you will conclude that the mirror image person holding up what appears to be a right man think when I hold up my left hand. Another thought is what if we'd enter the universe which was not orientable. I hold up my left hand and I look at it and I think that it's left hand, it's left hand. I'm transported around the universe and I'm coming back and And then, lo and behold, I'm holding out my right hand, and I'm still uttering the same words, this is the left hand, this is the left hand, but I'm now staring at my right hand, and when did the content of my book change, and so on. And that sort of argument has quite a nice parallel in the philosophy of time.

2:00:00 If you think that we could live in the universe, the Gurdjieh universe, in which there are close final lines, locally we would just like the universe to be known. So whether or not we actually live in the Gurdjieh universe as a urban, the local physics could be the same. And likewise, the oriental or non-oriental space, in a non-oriented universe, but we could do it, although the physics would be the same. There's been a glitch because the recontractions presumably would not be operating if we lived in a non-oriented universe. No, there's some issues like that. These are just intuational parts. Okay, so that would be a relationist account of pantons, of what it is to do left-handed. And really, of course, the work that's being done by the left-right distinction, these do not exist as intrinsic distinctions, but rather as the relations with homeroid and anti-comment, and those are what are really carrying a content of the left-hand decision. Now, all of that is fine. Now onto my last and final topic, and the one where I say there's a real problem. Well, there may be a problem, I mean I think which is parity of our nation. Now the way towards parity is harmony, then there's no problem, then the generalist picture is fine. The generalist picture only requires that we identify states of affairs which are related by black centuries. So if he is not from the black century, then the left is not identified by the right, We've got that common sense understanding of the left hand is differing intrinsically from the right hand. The thing about the general description is that it also requires that where there are distinctions, we can characterise those distinctions in an incredibly transparent way. so how is it that the equations characterize the weakly decay process which is handled, how do the equations manage to pick out the process of the one sort so decaying in a less handled way from the process that decays in the right

2:02:30 manner So the equations have to pick out the difference. What about, if you do this in one dimension, one spatial dimension, the answer is trivial and uneasy. It's very easy for equations to characterize one direction rather than another. Well, this is something that philosophers would be very bad at. I have in my mind, he said that Einstein and Captain Agnes, where he said that Kant's problem arises away for the one-dimensional case. And Kant was pretty bad at, because he said that the problem arises in the case of time. The Discussive Concepts can easily pick out a one-dimensional direction with real numbers. The positive direction is that in which the difference between the two numbers, if you take it this way you'll get a positive number, if you take it this way you'll get a negative number, And the positive way is the way in which the difference squared is at the same sign as the difference. And the negative way is where the difference squared is at opposite sign to the difference. So that is a purely intellectual, totally transparent, mathematically well defined way in which you can pick out orientation in one dimension. And what's more, it's exactly what is used. And if you had a Hamiltonian saying which was where the potential was something like this, then it would be a parent-violating interaction from one spatial dimension, and everything is totally clear. So, for that reason actually, time-inversion-violating physics is mathematically you can characterize it without any problem it's just one dimensional direction it's very easy to write down directions that signal out a unique direction in time it's mathematically well defined and so on now in two dimensions of course spatial inversion is just a rotation so we wouldn't expect this

2:05:00 I mean again though one can still give it context You can always just choose a coordinate system with linear coordinates in two dimensions and then specify the difference between one direction and another in terms of that coordinates. Mathematically you can get a content. I do think there's an issue here that in mathematics we can give particularity to a lot of things that we don't really know how to give physical content to. But that's, I suppose, only to say that we don't, but physics that actually makes use of this mathematical resource just isn't the physics that applies to the real world. So, it's not some absolute physics. By its nature, it's not particular in the way that mathematics does, because it's contingently so. So physics turns out not to use structures that are available in mathematics. There would be a gap, for example, in a unique dimension, or a unique origin, or a unique point in space, which is the point I. So there's a contingent in physics that doesn't make use of those resources, and it does make use of resources to distinguish these values. of course in two dimensions we can consider this and now it's not clear to me that we even have mathematical resources to give content to this well we can give content to it in terms of this is where I'm starting to get into trouble But if we now work in Euclidean space, where we factor out rotations and we have an invariant notion of a two-dimensional Euclidean space, I don't think we can give content to the notion of a handed shape and the mirror image handed shape. I don't think mathematically I can express the distinction. In odd dimensions, R goes to minus R in odd dimensions, I don't think we can give mathematical confidence to this distinction. Sure, you cannot. I mean, I'm actually... I'm not. I like to be over-minded about this, but if anyone knows of any way to do it,

2:07:30 and I wouldn't be delighted because it's solved by problem, but indeed I think not. In physics, that's what, that's why I think it's a good problem. Well, the point is that in physics it seems we do distinguish this, and now this is a problem, because it seems that in physics we have equations which select out the shape of one handedness as opposed to the shape of the opposite handedness, even though in mathematics we can't. So the issue is how do physical equations manage to do this? Now, there is one way, which is constantly, which destroys the general description, which is to say the equations have got to have with them some little picture and we've got to actually look at the little picture in order to understand which of the two shapes the equations are picking out, right? And, indeed, you pick up a textbook from Electromagnetism used before you go to university, and it'll have things like the left-hand rule and the right-hand rule with little pictures of hands. And that's how you work out which direction the current, you know, in the field. And those are the pictures that may even be in a sort of introductory undergraduate textbook where you have a text of calculus and a cross product and so on. So the cross product, the vector product of two vectors, you know, so A cross B, what is that vector? So, to make precise what that vector is, you usually refer to the left hand rule. You actually have the word, the first finger is a line, the left hand is a line in the direction of A, the second finger is a line in the direction of B, the thumb towards the left hand. Now, if that's how you give content to the equations used in physics, then this is exactly Kant's, this fits into Kant's equation. And it's to say that intuition's play, you know, literally you've just got to see the thing, you can't intellectually understand the thing, you've got to see the thing in order to make sense of... And to see how that really hits home is, if you imagine describing yourself in the physics,

2:10:00 and you can do this in class of electromagnetism, you don't have to go to the capsule, just do this in class of electromagnetism, describe yourself as a distribution of charges holding up your left hand, and say that the cross product is the one where the vectors are congruent to this hand, then how do you characterise the left hand as the one where the cross product is congruent to, as opposed to the right hand? If you were to do it, somehow that would mean you would mathematically characterise the left as opposed to the right. which, mathematically, it seems to be impossible to do. Can I just say that the problem is just as bad as charged conjugation because charged conjugation is diagnosed with minus i And now this is an automorphism of the complex number field. I mean, this has no imaginable content. What one come up is that we characterise the imaginary unit as the positive imaginary unit, rather than the negative imaginary unit. That distinction has no mathematical meaning. One could, of course, propose an imaginary unit with an imaginary unit amongst its sign. one can't say what it is about the unit itself except for the positive value as opposed to the negative value. I do have a suggestion that this is a problem and I would like to solve this problem and if the answer is we have to give up the generalist picture then so be it. if I want to just pop this through to the truth of the matter. You know, I'll tell you what's going to come to you. I do have a suggestion, which is, originally I thought I had a solution to this some three or four years ago, but one of the bully convinced me that that was wrong. I would turn for the honest solution was wrong. I now think the honest solution may be the right one, But I do have a line of thought on this. Before I do that, I just want to show how there is a bit of a subtlety in this, as to what physics really gives us.

2:12:30 okay so first of all let's look at the simple case of p violating c violating the pc symmetric theory so we can track some physics so here's just p to decay and what we have at first is a situation where we have a phenomenon where the majority of electrons are emitted in the downward direction. And we have a clear operation procedure for defining the left hand as opposed to the right hand, namely track the motion of the circulating electrons in the current with your fingers and orient your thumb in the direction which the majority of electrons are emitted and that picks out the left hand. That's clear, isn't it? My shadow won't help. I curl my fingers in the direction of the current and it's down. If I take a mirror image in the plane here, then I write this picture and this is what is forbidden. We don't see this process. If I take a charge conjugate is still spinning in the direction shown. Of course, the current really is in the opposite direction now because in C-contrary, I've got a positron around an electron. So the B-field is reversed. The B-field is not directly observable. Don't worry about that. So now, if I coil my fingers in the direction of the moving electron and my thumb is in the direction of the preferential emission of electrons, it's my right hand. And now the point is, the idea is that maybe the law just says It says that charge of knowledge between the gate processes are oppositely oriented. That's what the law says. It doesn't say any more than that. And in order to say that, it doesn't have to distinguish the left from the right. Okay, so that was my thought up to, whatever, three years ago or so. But it only convinced me that that's not really good enough because the fact is that the state of affairs

2:15:00 the P inverse and not the C inverse is excluded by the law. The equations are ruling out this process here. So how do the equations rule that out? Well, I'm not going to address charge communication because it's too hard for me now anyway, but I don't really know. Let me say something more then about p-violation with a p-t-symmetric theory. So here, this is just a nice classical model of a p-t-symmetric, p-violation and t-violation theory. So here this is just a magnetic monocle, just coupled to classical magnetism. and now you've got the monopole sitting in the middle of an electric coil and it's going to be accelerated axially along the axis of symmetry of the coil so here I've got the monopole mass and acceleration it's equal to the monopole charge to the B field the B field is going to write in the key in terms of the cross product P value in theory has the cross product in it Let's see. And now it's clear that this is picking out, I align my fingers in the direction of the electrons in motion, my thumb in the direction of the acceleration, it picks out my left hand. And now let's look at the PT process, so here I've got the P mirror imaging, the acceleration is inverted but not the circular motion, and now I take the time inverse process and now Now, the direction of the circulating electrons has changed, and the acceleration has not changed. The acceleration is invariant under time reversal. And then I'll, well, if I worry my fingers in the direction of the circulating electrons, and my thumb in the direction of the acceleration, it's still my left now.

2:17:30 So, what's going on here? I'm supposed to figure out my right hand, okay? Do you mind if I insist on an answer? I really do insist on an answer I'm sorry I'm not going to tell you you've got to come up with an answer this is a PT inversion I just performed I started off with something What is the theory that we're considering? I thought we started on PT and theory, but we're not talking about CPT. This is the theory. So PT is symmetric, the theory which values T and values T. You have the full equation of motion on the board. We did a p inversion and we did a p inversion. And we ended up with the same thing we started with. We ended up with the same thing we started with. It's just rotated. And why are we concerned? Isn't this exactly what we wanted? We've inverted T with inverted P. We've inverted P. So we start off with something characterizing the left hand, we share that with something characterizing the right hand. Why don't we do a P inversion? And then we do a T inversion. It's a PT symmetric theory. This is allowed. The fact that it's 180 degree rotated is allowed. That's not the problem. The problem is why is it picking out the left hand whereas if you've performed a P inversion you ought to be picking it out of a racket never just leaves the room

2:20:00 We're all happy with the situation. You're going to have to do a little bit more to convince us that we should be troubled here. Someone else is going to have to try to... So, in the PC case, we started off with a situation. We ended up with a PC inverse. The initial situation characterizes the left hand. The final situation characterizes the right hand. In that case, we had a PC invariant theory. I think we have a PT invariant theory. We started off with a situation characterizing the left hand. We ended up with a situation. Okay, but the T here is a time inversion. Is that actually fair as far as characterizing a temporal inversion in terms of a spatial rotation as far as hands go? Well, are you questioning the move from here to here? Well, as far as, is this supposed to be temporal? So, I guess the point is that in the reversal of time of the direction of motion of the, what was it, a magnetic monopole? Yeah, this is a magnetic monopole. The acceleration is unchanged by the revolution of time. You're almost there. There's something missing. Congratulations. Okay, so I think you're almost there. Here's my answer. I wanted you to worry about this because, frankly, if you don't worry about it, we won't believe the solution anyway. The solution is remember the prescription for how to determine a hand in this, whether it's left or right hand, is point your fingers in the direction of motion of the orbiting electron. What that means is keep track of the tip of your finger with the position of the electron as it rotates around. Now, in the T T-inversion, you have to T-invert the process of keeping track of the motion of your hand. What you really need to run here is a human hand aligning itself with that rotating electron

2:22:30 in the reverse direction of the time. What that means is it's going to be someone curling their finger in the direction of the electron in the reverse direction of time, which to Because us, in the forward direction of time, is uncurled by the hand. And the hand you have to uncurl in order to keep your fingertip positioned at the electron when your final direction of acceleration is your right hand and not your left hand. I really want to have a PowerPoint presentation, because now I can run a slideshow, which shows the thing happening. But you can do it painstakingly by drawing lots of pictures, if it were, and then run me to make sure you're backwards. you say that the anointing represent the thing you have to actually make your hand do something in time and then you're saying that's reversed but why do you have to do that why can't you just say I have to hold my hand statically but then curve it appropriately to represent the motion synchronically as it were the direction of the motion being given by past is the knuckle and future is the fingertip. And that's then synchronic. I'm not moving my hand, but I'm still, that's what I'm using to represent motion. I can only say that if you actually try to depict the observer positioning her hand correctly in this way, in a linear sequence, then what we've got here is a single sequence of events which is allowed. Okay, now you can read it forward in time, and then you can arrange beside that a sequence of pictures of someone aligning their hand,

2:25:00 such that their tips of their fingers do follow the motion of the electron, and it will be a left hand. Now, if you draw beside that sequence, someone landing their hand, such that that condition is satisfied, the tips of their fingers are adjacent to the moving electron, and in the reverse sequence, they can read the sequence the other way. It has to be a right hander to draw. Okay. Well, the point of this is to say that whatever's going on in the way that this characterizes the left-right distinction, It's not quite a static, three-dimensional thing. This is, irreducibly, a four-dimensional process. And I'm not sure whether this is the key of a solution to the grid or not. It's something that I think one has to understand rightly in order to be sure... I have a slightly different, I have a solution which is not directly abolished. This is more fun. I think it's fun. Maybe I'll go to the understanding of the PC case later. Is there two of us that now? Okay, so, I think, it's a great angle. I'm not sure how it's right, but it is this notion of an orientation field. Now, what if you stick an orientation field into the physics, into the equations? Now, this is something that, for example, Bob Wald explicitly says we have to do. This is in his book on general relativity. If you stick an orientation field into the physics, And you've described the weak attraction process as congruent to that. In a sense, one's not known, because how do you characterise one sense of the orientation for a rather than the other? This is why I thought it was a normal solution. This just isn't getting us anymore. But think about how do you characterise an absolute position in space? Now you can do it in the other, say it's a force or solution, it does pick out a unique, or a unique, if you take a standard case, it's really all time of time, but you've got the singularity, which is unique.

2:27:30 And I think by extension we can see that you can define a field, not a manifold, which is somehow singular or has a distinguished value of the field, which picks out a point, and you can refer positions to that. And this, in a sense, would give you an absolute position in this text. The field with the singularity in it does not itself have a position. That's the key thing. It's not that you've got to specify where that field with the singularity is located on the manifold. That's a non-question. It's rather that you then relate things to that. Now it might not work the same way for the orientation field. It's not that the orientation that is left rather than right. It's that by being a nation to which comrade or anti-comrade that carries the physical continent. And the orientation field itself does not have to be either left or right. Now I think where I was going wrong with this is because if that the case you would end up with a theory that was P-symmetric. And I thought that was somehow not allowed. But I think maybe this is the right answer. And it is a theory which is P-symmetric. So in other words, this would be to rewrite the lecture weak theory using explicit orientation to it in such a way that it is P-symmetric. And the P-violation business It only means that the weak interaction is picking out an orientation congruent to, or anti-conguent to, as the case may be, that orientation theory is. And that is where the B violation resides. The entire theory is now a B symmetric theory. And now what is the physical content of being congruent to, or anti-conguent to, what is the content of that answer? it is in spelling out whether the weak interaction takes place delivering electrons preferentially such that the fingers of the hand is on the side of the human heart.

2:30:00 a totally contingent, non-generational fact about the universe, and it's as trivial as that. So that's the suggestion that I wanted to go back to. Okay, so, and instead of how to pick up a T violating part, that's easy, we can do it just in the way that I didn't gave it. You can characterize the direction for the one dimension of mine. Okay, so to say it again, the solution is that it's correct, that there's nothing in the left hand and on the south that makes it better than the right hand. And what we mean by P-violation is no more than that there is an explicit... that these processes have an antivist and it is always comparable to each other. And you can explicitly introduce this orientation field and thereby define the process locally as congruent or anti-congruent depending on how you stuck it in. And the arbitrariness with which you're sticking in to make the culprit or make the culprit is the arbitrariness with which the unit heart is on one side vis-a-vis the wing decay process rather than on the other side. And it's the same arbitrariness that goes in the design position in defining the cross-product. So, so that's, that's, that's, that's, that's, okay, and just to fill it in, using the cross product in this way, conceding this orientation field, having explicitly eviolated theory, is going to Kantian groups, right, and it's kind of like a quick and dirty way of doing the deed, but the right way of doing the deed reserves a generalist, it is to introduce the disorientation field. Sorry, I've got an obvious sort of question. The connection was, excuse me, with structuralism. I mean, one can understand, we're going back to your stuff on identity and discernibles. I mean, Dean and I have mentioned this in our paper

2:32:30 in the Ellen and Catherine volume. We can understand what you're saying in structuralist terms if you understand these weakly... Yeah, and irreflexive symmetric relations as, in a sense, constituting the objects and thereby you save PII, but it seems to be very structuralist terms. This spell out then how it goes all the way down to the end. Do you see your whole generalism as union kind of structuralism? Because one could say, particularly with the introduction of the orientation field, what you're doing there is saving the generalist picture by introducing an extra structural element. And that does the trick for you. It does the trick that, and again, I don't want to bang the point about Vile, but he, part of the reason why the ego and the indexicals are still in for him, I think, have concerns, but these sorts of concerns, and that's why he in effect would reject the generalist picture. But is that a correct characterisation that you essentially save a sort of structuralist understanding of your generalist picture through the introduction to this orientation field? Yes, and I think it is saving the generalist picture. When you use the word saving, it makes it sound like It's resolving the problem that arises for us. It's resolving the problem, and I think it's showing the sensibility, even in this case, of or something that is okay. Really, this is all about insufficient reasons. It's not really about anything else. Is the intellect enough? Do you have to resort to some sort of, something given in the intuition? I think Vile, and of course Vile is on record as rejecting the left-right distinction. And as far as introducing his orientation field is rejecting the left-right distinction, it's a sort of standard. I only thought he'd not have, so I'm not sure that here he would be going to... But can I just say something about the general constructors this year? I mean, look, there's been a very difficult talk this morning about how do structures correspond to the reality.

2:35:00 And I think that there's a way of short circuiting that a little bit, which is to say that the problem is the same as the problem when we talk with tables and chairs. We make judgements about if there is a table or a chair or whatever. How do I correctly make a judgement like that about an object in front of me? Now I'm not suggesting that problem is trivial. But I think that there are various resources that you can use with that. Now I'm saying that it's that sort of problem going on in physics. In physics, what goes on is we make judgments about what objects there are, they don't have a conceptually available, but they are judgments of the same sort and express them in predictive terms. But here's where I make my pitch. We make those judgments in the light of physical which are not linguistic at all and have nothing to do with predicates or judgments and forms of sentences and so on. And this is how I would call myself at a deeper level of structuralist. I think that the sort of understanding of what happens in the physical world through an understanding of the mathematics you've actually used in physics, I think there's a genuine understanding there. And we, in a fragmented way, cash that out in terms of sentences, propositions. And when caching out in terms of propositions, we have to use credit cards, we have to talk about objects, we have to use the identity. And I'm suggesting PII is a technique for correctly using identity. And we do it as best we can. We do it as best we can. In the light of our mathematical understanding of reality, we abstract out predicates. We use predicates. And we do it better or worse. And the better a physicist you are, the better you do it. And the worse a physicist. And the worse you do it. So you'll say, you know, there is an electron, there is some processing process, there will be nouns and verbs and so on and so on. And what makes that true is that the world is deep down about objects in it.

2:37:30 What may not sound as true or not true is whether the physics, the way mathematics, supports that one well, how well you've done in interpreting the sort of theory. And at the fundamental level, what the world is really like, is like what the mathematics goes with today, which is not in terms of what you should do. So, now that's a bit of a cowardly way out, maybe, because I'm not saying, look, here's this mathematics, and it's a structure, and a structure mirrors the structure, you know, I'm not saying that, I'm saying this is the mathematics, and understanding the mathematics, and the other physicists, do you understand reality? but then there's talk about reality which uses objects and adjectives and so on which is conducted to better I don't know if that's I wonder if we'll be glad if this is more of a discussion I wanted to ask about your disagreement with Dirac and Bohr and Bob and perhaps I didn't quite understand your position but It seemed to me that those three were right, that you're wrong. And so I wanted to ask you, so it sounded like you wanted to say that what we see is real, and what is real is invariant. Now that strikes me as impossible, because if you and I jump in our spaceships and are traveling at great relative velocities, then you look at my spaceship and you see it foreshortened or perhaps better rotated but okay and so you ask how long is this so then we ask well what about the length of the spaceship right and I will say that the space is 50 meters long you will come along and say that's 25 meters long that's what we see but that's not invariant neither of our answers are invariant And so I take it this is what we're pointing at. We do disagree. I mean, what I see is, in terms of black rays that's still on my retina, that's all perfectly really and invariably described. Now, what I attribute in terms of the length of the rock,

2:40:00 well, we describe the length of the rock in terms of the invariant interval between events. And that invariant interval between events is, for the raw emotion, the invariant interval between events will be less than the invariant interval between events for the raw breast. Now how come? Answer. The events are different. The events I would choose as being irrelevant ones, the natural ones to take as demarcating the length of the raw will be different for me than for somebody at rest. We agree that the sensations will be invariant, and so far as you're just observing there, and you have your particular brain station, so certainly the sensations are going to be invariant. Right. And then, um, but then perhaps the question is, well, what is it that, I guess, I mean, a lot of work is being done here, or perhaps it sounds like you want to make an option of what we see or what, um, what's going on with C, right? because especially for someone like Bohr and probably the others too we're talking about properties that we attribute especially Bohr wants to say that the properties that we attribute are certain classical properties in this analogy for example in relativity theory between what we have to divide up between space and time we're always going to have some sort of rock we're always going to have some sort of rock we're always going to have some sort of rock which does the same as a conceptualizing thing in terms of invariant space-time distances or something Now we might not be convinced by that, but that's presumably what he has in mind, but especially once you start talking about what we see, well, there's a distinction between our sensations and what we see, or at least oftentimes, and what we see, you and I have different sensations, and then if those sensations are supposed to be picking out some situation, well, as long as we're careful to use those sensations in such a way that they capture what is invariant.