Gauge Theories & Loopy Locality (contd.)

0:00 Thank you. covariance theory of ultra-magnetic co-variance. Then we discovered all of these complications. We just start with theory and we ask, what is its ontology? So what's the stop us from taking a given quantum field theory and just saying, what is its ontology? You're getting like how you can start with it? Nothing, nothing. I mean, that seems like a good way to start, at least. And then you can postpone until later what the relations are between the ontology and the Sure. I mean, in some cases, there is a certain equivalence. I mean, there's one way of giving a loop representation of classical pre-Maxwell field, sorry, of the quantized pre-Maxwell field, which is unitarily equivalent to the usual Foxquakel representation. So it would be sort of nice to have a story about how those two fit together into a single picture of the work. But for the others, we can postpone them, maybe. is there a fairly real thing in which you could have imagined yourself stumbling upon the right one without having to go by this route of saying well there's an approach that other people use that I'm trying to get away from I've got this approach and it's got this whole bunch of things and I'll pick this one because it agrees with you is there a way of picking that one without just doing so because you know I will agree with the one that you're trying to get away from The motivation you're talking about there, I mean, all the tryings, is that supposed to be motivation that comes from the idea that we want just one quantum field theory at the end of the day? Or is it a motivation that's supposed to be coming from, say, my prejudice for a non-separable story? I get it. It's just trying to paint like what Harvey did, but you pick one and you use it because it works eventually. There's a bunch of choices and you pick one and it works and you stick with it. Right. Okay.

2:30 Obviously, now that we know this is the loop proof that's equivalent to doing things that's otherwise, then we can say, well, we'll pick that one and look at works. Is there any, no, it can't really be more than an intuition, but is there any way when faced with all these loop groups of guessing that that might have been the right one effect from the offset? Well, the only thing I can say to address that question is just to repeat the quote from Aishem and Ashtaka, where they say that in a certain sense, one of the loop representations that turns out to be inequivalent to the usual folk representation, looks more natural. as far as non-abelian gauge theory. But that's pretty much all they say, and I can't get deeper than that, or can't even really explain to you why they say it. So, my question at the end here was, what does this imply for the question of whether a quantified general gauge theory is local, but non-separable? And here, you know, I'm really, I don't know how to ask that question, but here's a suggestion. The suggestion is that the answer is bound to be highly interpretation-dependent. Suppose you're a Bohmian, then you might, for example, take it to some particular loop representation as the appropriate one. You might, I don't know. And that a wave functional in that representation gives you, for example, the probability amplitude that that particular loop carries a loop-like classical excitation of the connection along gamma, or perhaps that a pre-telelectric field is associated with gamma. This is the kind of thing that Ashtakar and Ravelli speculate about towards the end of their paper. If you took that line, then maybe pre-quantized electromagnetism would appear to be non-separable, but then you still have all the usual issues about Bohmian non-locality within that approach. On the other hand, if you are more inclined to a Bohrian interpretation of quantum theories in general, you might argue that all these various representations are complementary. That's what I was actually alluding to earlier. What does that mean? I don't know what that means. It means, don't ask the question, what is the world really like? But I mean, at least with Bohr, what was up from it? I said, look, when you're going into the larger, you see people either measuring something like

5:00 trajectories of properties, or you see them measuring wave-like properties. Then you convince yourself that these two things are mutually exclusive. So at least once you know what the experiment and setup do, then you can use the language appropriate for that setup. That I understand, but this notion of complementarity seems very unconstrained. Well, to plug it into the Goryan framework, I agree. We would have to somehow operationalize some sort of procedures would elicit one of these representations rather than another, something like that. But in a sense, that is done by the literature and by Keprin and Halvorsen. In the case of the Rindler Quanta, that's true. I mean, they talk explicitly about number of operators in each one being, so to speak, undefinable in the other. And the literature talks explicitly about detectors that accelerate along these constant acceleration lines. But in this context, this is quite different. That's a completely over-question to me. But you're right. I mean, neither of these alternatives, these are just hand-waving. I mean, whether it leads anywhere or not, I don't know. But could I make a comment related to, which I was half going to make earlier, that, I mean, I remember in algebraic statistical mechanics, they get these inequivalent representations which differ by the value of some global observable like the temperature. And it's obvious that the sensible thing to say is that the practice of modeling, you know, take a moderate view of what you're doing in scientific description, the practicing physicist needs to choose the representation appropriate for the system they're studying as given by the values of these classical super-selecting global observables. in that sense the admission of inequivalent representations is compulsory and they're all physically useful, they're not all physically real at one and the same time with the same system, but they all need to be in your theoretical tool your theoretical menu of descriptions to describe today's experiment and then concerning the FOC for EM I vaguely remember that if you had started with one FOC representation you could build another Fock representation that was not unitarily equivalent by taking as the vacuum state in your

7:30 new one, coherent state of your old one with its infinite exponentially dying tail. Now, if that memory is right from my slight study of these things, then couldn't a case be made for saying, well, the EM field, quantum EM field, gets into different sorts of regime. And I can imagine on Tuesday, getting it into a regime represented by my first given representation, but that there will be other notions of excitation which might get physically relevant or salient, in which a vacuum of this new notion of excitation is actually given by a coherent state of my old notion. Now this is that, the physical usefulness on different days of inequivalent representations, just like my statistical mechanics. we seem to be saying that electromagnetism is non-separable on physics and physics so it's separable on money from women that seems a little uncomfortable why is it, but that would require one to show that concerning these inequivalent representations one of them was separable and the other not I thought that was a little that's not yet no, you're right, I'm jumping your head but do you think that will turn out to be true for these different Ashtar Karajan things that's speculation But I mean, but maybe I can add a little bit back because it is, and I've been looking at particle creation in various backgrounds and there are lots of situations in which technically the state's bank idea would at any time is completely unitary inequitance to the state's bank that every other time. But it's always because of some convenient typical assumptions, such as a spatial uniform electric field. The reason you get the zero as the probability of, you know, as the inner product between two bacteria between different times is because as soon as the probability per unit body drops below one, your assumption of spatial uniformity makes a zero. So there are lots of situations in which technically your, you know, your spaces, if you just build them up from a more abstract cultural perspective, you'd conclude that these were unitary and equivalent representations, and you'd be very worried about whether or not you could make any sense of the dynamics that moved from one to the other. But when you know what's

10:00 actually happening, you don't have to give a second thought to this unitary and equivalent thing, because you know it's just a problem for the mathematical details and not a problem a gentleman physicist would have to compare themselves with. Is there hope that this kind of unitary inequivalence, if we understood on a more physical footing, we could, you know, we could match two unitary inequivalent things up and say, well, this piece is close to that piece, and this piece is close to that piece, and the infinities have just become the best. Well, I think that it's that hope that we could present this package to the physicist in such a way that the physicist would know what to do with it comfortable doing the right thing at the right time. But I'm not clear that that's going to be enough for the philosopher. He's worried about what the theory is telling us about what the world is like. He says, it's definitely time to answer that question in order to do physics that's fine. So I'm still worried about what the philosopher's book is saying about. Even if the physics can be presented with a very useful tactic that will do everything he wants to do. I'm almost done. these are very interesting questions I don't want to cut you off as you can see we're already sort of heavily into speculation here, let's go a bit further suppose that we got some sort of story about free gauge theories we're supposed to be interested in issues of locality and non-deferability and locality certainly has a causal component and now we have to be talking about interaction because that's where the causal point is going to come in when you're talking about a gauge theory. So, if we look at the strong-electro-weak interaction described by non-abelian gauge theory, are those interactions local but non-separable? Well, I mean, simple answer, I don't know. But let's see what is relevant to answering the question. We describe interacting fields usually by including interactions in Lagrange and Hamiltonian theory. And these couple the gauge potentials in the matter field current at the point, which is sort of interesting, where you could charge scalar field 5, then you stick a term like that in Lagrangian, well sorry, like that in Lagrangian, where that's the current

12:30 associated with the matter field. And in one sense that interaction is logical because these things are evaluated at the same space-time point. Well that's nice, but so what? It doesn't represent anything physical at that space-line point anyway. If you wanted to defend a local and non-separate separation of interactions between a gauge field and a matter field, you'd like to be able to formulate that interaction in terms of homonomies rather than connections. I haven't seen anything like that. Given what has already been done to reformulate three field theories in terms of homonomies I would be hopeful that it would be possible to do that with interacting field theories as well, but I've not seen anything like that. I don't know what to do with it. If any of you have seen anything like that, please let me know. Even more speculative, and this is like one minute and I'll shut up. What about quantum gravity? Luke played a big role there in one approach. Rebellion, Smolin, and other people who applied direct quantization and the general relativity experts that actually have a new variable, one of which is a connection theory. And they've studied loop representations of resulting quantum gravity theory. So what have locality and separability looked like there? Well, who knows? But it's an interesting question for the following reasons. Insofar as I understand the program, the theory is supposed to be constructed without a background space in time manifold, which is supposed to somehow or other emerge on these approximations If that's the case, what do we mean by local action separability? Because those are principles which seem to presuppose some sort of space-time, otherwise they're not well defined. Well, maybe, there's hope, after a loss of loop, if the notion of a loop makes any sense in this theory, there must be some manifold in which such loops are defined, even if it doesn't have a metric in between. If that's the case, then maybe there's enough structure in that medical even in the absence of a metric to make sense of some notion of locality and separability and to apply it to such a theory and see what happens when you do absolutely thank you Richard can I make a quick remark about that last

15:00 just a little remark I think that your closing paragraph to my slight understanding these matters. Your closing paragraph gets it right, and your penultimate one is a little bit worrying unnecessarily. Yes. Because I don't think it's true that loop quantum gravity only has a manifold an approximation. There is a manifold throughout. Yes. What's characteristic of it, and much heralded, is this feature classical GR of the manifold being dynamical rather than being a background or a canvas or non-dynamical or independent. So it's not so much that it's without a background space-time manifold. It's without a fixed canvas space-time manifold. I think there isn't a problem about the existence of these loops. It's not that the notion of local action thus becomes immediately ill-defined because what is time anyway. What is dynamic about this manifold on the picture that you're thinking? Oh, that it's dynamic in roughly the way general relativity is. Well, I mean, it has a metric, and the metric is more like connected to something like the meta-distribution. Broadly, yes. I mean, the metric is quantized, though admittedly in these new variable and there is flavor that there ain't a manifold arises from an interesting feature that you get these volume and area operators with a discrete spectrum but that's not because there is deep down in the basis of the theory at the very beginning a granularity of space time there is a manifold I mean, that strikes me an interesting, I mean, I don't really understand this stuff very well, but my understanding of, for example, Wheeler's Superspace, there wasn't this space time in that world there, that that itself had to be, one hope, a reconstructive approximation from, is that wrong? Right or wrong?

17:30 Right. Okay. If that's the case, then what you're describing is actually less radical than Wheeler's program in that respect. Well, I think there's a three manifold. There is a three manifold in Wheeler. I'm sorry, there's a three manifold in this. Oh, is that what you're saying? Yeah, a three manifold is all we need to make sense of a certain kind of separability. Yeah, right. I haven't even read that stuff yet but it sounds, from what you're saying the metric of a quantum entity defined on a three manifold that what you would have from the outset is a bunch of three labels three numbers, you just define each point to label the points but it's not a manifold until you take something like a mean field limit on the metric. Because until you've got a well-defined metric, then you don't have a well-defined... Well, you don't have a well-defined sense in which the manifold is some curved space on which we live. It's just a bunch of three labels that we do to define things, to label things until we know what they are. So it has a dimension, because we have three. Yeah, right. So all we know is that we've got that you need three labels, so you need to specify each thing. Yeah. But you don't... I think that's true. dynamics or live on a curved three-spane until you take a semi-versical limit in which you can make sense of what the distance between two such points would be. I think that's fair. So you have the continuity and differentiable structure of a three-dimensional manifestant. Oh, okay. But you do not have the physical interpretation of the metric as giving you ruler measurements. really, until something clever is done, like Yes. So that's why I was stressing that I don't think there is a kind of ad initio granularity of space, even though there are these discrete spectrum error in volume operators. But anyway, that was just a slight remark about your final slide. Thank you. Thank you. Well, again, I apologize, but if someone can go here and make sure, I hope it's something

20:00 that you found interesting. Oh, yeah. Masses of it's interesting. I didn't say it at all. It just seemed like a massive of good points, but inevitably a few open questions. Yeah, I was just a question if you can comment on your thing about the interactive gauge theory, and it seems that in a somewhat non-constructed way, we can assume that any quantitation you're going to have, or if the theoretical form of the interactive gauge theory is going to satisfy the criteria, because that theory is going to consist of something like a wave-functional or a configuration theory, which is invariant under the Glass-Full-Gate Translation. And we know, like you were saying, that there's a nice, long, long map between the Wilson loops and the connected to that gate transformation. So we can regard the Wilson loops as just being a quantization of the space of connected to that gate transformation. We've got a way to function on the space of connected to that gate transformation. We've also, it's a practical way to function on the space of the Wilson loops. So there's a sense in which we don't need to look at that set, but they're probably that way, the sense which we want to jump in, in any way, in that context. At least all of it. That seems right, but I can't quite see my way of writing down all the steps. The usual way to proceed, you write down interactions in the Lagrangian, with the A and the J. Now, that is going to be gauging variables, Lagrangian-Graniches anyway. What I would like to be able to do is to write down some other Lagrangian. It doesn't even include A at all, but includes a whole on the other. And if I couldn't do that, I would somehow feel uncomfortable. Are you telling me I shouldn't feel uncomfortable, or it's not that hard to do that if you know what you're doing? I think it's the form of... I guess I'm hardly... ...that arguably, if you've got a quantum field to satisfy that requirement, you actually don't need to ask things about what you got it from. So even if there's no context... Because we want you to be able to consider some sort of quantification between maybe a So you take the classical loop thing and get down to the quantum thing, yeah?

22:30 That would be nice, but it seems that we shouldn't be too worried about how high it's actually. The actual logical direction should be to start the quantum theory obtained by whatever. Take that as possible and then go back with the classical theory. And in that case, we need to worry about the loop. Go back with the second thing, but what do you mean? Well, in the sense that we should regard the classical theory as validity as follows, Right, but all we know is that we have an interacting theory, a theory of interacting field, which includes a gauging variance for Grantia, and how do we address the question of whether the interaction described by that theory is local or not? That's what I'm not clear about. And that's the question I'm trying to ask. If the theory is formulated in terms of structures like a connection, then I don't know how to address that question. It's something like a one-functional that assigns amplitudes to certain Wilson loops. Right. They're all about what we can go about with pro-way connections. And then we can just say, well, what sort of correlations are there? What sort of permutations are there between operators? We can do all that stuff, sure. So if we think of locality in terms of permutations for operators, that's okay. Okay, so what's the... And that's not something I've been talking about today. in a completely quantum context, I give you a quantum field theory, what's your criteria for what's the reality for it? Well, I mean, I was working with those two initial principles, local action and separability. And neither of them, as it stands, is happily applied to a theory until you know what the objects that that theory describes are and what their properties are. And if the theory describes objects which themselves, for local actions, if the theory describes objects which can't be happily said to be spatially separated, then we can't apply the principles. So two things would happen there. We could somehow make it a constraint on our interpretation of the theory that it eventually tells us

25:00 that there are spatially separated objects, and then we can apply the principles. Or we could say, work, because we're not dealing with the theorists in the industry in that way, and then we have to cast around for alternatives to that principle, capturing some sort of intuitive content of locality, and certainly that permutation of operators is relevant there, but if you like it, there was something a bit closer to the principle of locality that I think is there. Yeah. I wonder what the assumptions of locality and non-severability, are they Do you want to have an interpretation of theories which are local and non-separable, or in this context do you see here we have a nice case that is local and non-separable, or do you rather have that as a requirement for your interpretation? Motivations have to be put in the background, to a certain extent. I think it's bad if I look for a particular outcome, independent of the material that I consider. My position is, if the world were classical, at least partially classical, described by classical gauge theory and the quantum theory of particle models, then I am confident in my own mind, although I hope you don't agree with me, that would be a local but not better of the world. Now the world is not like that. So then the question is, what is it like? And since we had an interesting conclusion that seemed to apply to the world I just talked about, the classical or funny sensibility world, it's interesting to just raise a question whether that would be true at the front of them or whether something quite different would be true. And their motivations are irrelevant to see what happens. So this would rather be context where you test whether it's a sensible way to go to look for the precality and non-separability. And of course it could happen. I mean, it could be that the answer comes out clearly one way, it could have clearly come out another way. It looks, already, we might feel complicated than that. And another thing that could happen is that they question themselves, if that seems to make sense. and cannot be re-constructed in some suitably modified forms so that they look like they do make them, I think, with those.

27:30 Given that there is a gravitational analyzer for the private form, would you say that that's also the general activity in the month? Oh, that's really a good question. and Paul Teller and I spoke about this. I don't think the gravitational analog is as close as some people do. But, independent of that, I think that the notion of separability is actually remarkably hard to apply to a theory like general relativity. Why is that? Well, let me just try and find my transparency so you can see the problem. We're talking about space-time regions, okay? Now, as soon as you start changing something in a space-time region, the space-time region itself changes in general. So the idea of supervenience is tricky to apply. The principle of separability said that a physical process is separable in case, in region R, just in case what's happening in region R is supervenient upon the assignment of intrinsic properties at space-time points within R. Okay, now to test for supervenience, then, you have to see whether, had the property to those space-time points been different, the process would have gone differently. given that those space-time points are the same could the process have been any different from what it was but to make the process different in general relatively typically makes the space-time region different too so we can't really ask whether those space-time points have the same properties in a new scenario because there's no clear-cut way of identifying space-time points So the principle of separability is not really adequate to describe what's going on in that situation. It can't be applied directly. Intuitively, it seems like it should be approximately applicable. Because, for example, this is the case that Paul and I talked about. Suppose that what you do, you have your Hanukkah, the regular one,

30:00 and you kind of cut the curve through the solenoid. and then you ask whether or not in general that has changed various features of the space-time region surrounding the solar various features of things in the space-time region surrounding the solar if you crank up the current in the solar you change the stress-energy sensor so you've changed the Riemann curvature and now you're getting a different space-time subtly different Okay? So, what are we talking about? Is the value of this quantity the same as this space-time point? Now, I'm trying to cut the solar mode. Well, what space-time point? You can identify space-time points across different scenarios. In one of which the solar mode would have this current, and in one of which it has different current. So, we can't actually find a kind of support to that situation, interestingly. Now, your natural reaction is, well, gee, it's not going to make this space-time very different. Sure. I mean, it's still going to be basically flat with a tiny little regal there. So, surely we should be able to compare what's going on at the same point in the two scenarios. I share that intuition, but I don't know how to cash it out. What we'd like to do is have some slightly reformulated interoperability that allows us to apply to that situation. I don't have the risk. So it's not the fact that it's curvature, in fact, it's sort of dynamical curvature. Yes, curvature does, of course, it's dynamical. And the absence of this, this is a very important aspect, I would say, and absence of formal practicality seems to go into that kind of situation. The analogy seems to be, or lack thereof, between the two ideas that seem to be brought because in general relativity, we sort of know what's going on with the adaptation, maybe that we know that there are aspects of topology in the face-time that means that we can visualise by announcing by something of tones, of which to say that local blackness and non-combined number of topologies gives us more to these three different things as well. Now, it seems that if that would count as unseparable, where you weren't intuitive now, then that would make the notion of non-sepability really rather, well, with that case. So in those people think there's something interesting or non-sepability about the analysis, and that requires us to break the analogy between

32:30 the evaluation and the analysis. So I guess the question there is, what's your rationale for saying you do think the analogy is most of it? Yeah, let's see. I've got to go for a while. In comparing the different scenarios, one of which has a completely flat space, another of which you have one which is locally flat, but has your own topology or whatever. It doesn't have to be a topology, but the coaches can find this I'm reading if you're not considering it very much. Those are simply distinct facetimes. And so, in this case, I think that it's clear that we want the notion of separability, not the reality, because because there isn't any obvious way of pairing up points in the specific black space-time with the government space-time. So that's part of the story. The separability is supposed to pre-suppose. At least you can talk about roughly the same space-time point in the two different scenarios which are trying to compare. We're desperate for the separability to talk about. And that makes you come, clearly. Now, you could say, well, what if it's stupid away from black? And then I get stuck. And it becomes a stranger. Yeah, it's going to weigh that. Insignificantly different from . Do you want to say classical electromagnetism with quantum particles is not something? But you want to say that when you look at an analogous situation in general activity you can't even properly define the relationship of the galaxy. So that's really fundamental. Is that the asymmetry? That's not quite right. When talking about the gravitational analog, where we have two clearly distinct space lines, one of which is the other of which is the cone structure, well we have a pretty good angle on the cone. Those are clearly distinct space lines. I don't want the ordinary notion of separability, or even some modified notion of separability, to be applicable to that

35:00 comparison, because those are just distinct space-time regions. You can't compare what's going on in the same space-time regions in different circumstances. So it's not that it's...that doesn't show you non-separability, because the notion of separability is simply non-applicable to make that comparison. Okay. Now, the case that I was talking about that The case that we have the regular Harnas-Bohm effect with a slightly increased current in Solanoid, my intuition would say, no, no, no, I want to have some known inseparability, but I can have one in that case. Because otherwise, I can't even say that in the general Alphabistic world, the Harnas-Bohm effect is non-separability. I want to be able to do that. So I'm taught. I said what I wanted to do. And I can certainly answer the question, why is there no non-separability in the Harnas-Bohm effect? But what I can't do is say why what I say there doesn't actually show that, on my view, in the general alphabistic world, the Aharon-Azharon effect itself fails to be non-separable. Through inapplicability rather than through denial. Yeah, right, exactly. So I want to have a slightly modified notion of acceptability. It'll still kick in when making the argument, even in the end of this, in a logistic world, the Hara-Napong test itself works into the non-separability, but will fail to be applicable to the gravitational analysis of the Hara-Napong effect, just because the space-time's there so radically different, and wouldn't want to be able to see how changing things in the same space-time region does or does not. What about the alternative strategy of saying that the two cases should be treated in the same way? And that there should be non-separability in both cases, and that we should look for a slightly revised formulation of the notion of separability? Well, the trouble with that, I think, is that the Cone analogy can be stretched, or the Cone itself can be stretched in the analogy, as much as you like, which will give you a radically different space-time process, even though around the Cone is all white.

37:30 And it seems to me that I don't want to stretch the notion of separability so much as to be able to compare what's going on in those radically different regions of space-time in that case. Now, I suppose somebody could say, well, it gets the same with the homo-foam effects, so you put an enormous current through the solar matrix, right? And you could radically affect the space-time region there, too. I mean, the simple way out is to say, look, the interest in non-separability arises in a context when you're assuming you have a flat, non-dynamic background space time. In that context, it's no problem. It's quite clear how the form of sector might be non-separability. Then somebody says, well, what about general relativity? After all, in the real world, that goes on in dynamic space, like it or not, then the top line will be to say, okay, in the real world, the notion of that we're both in dynamic space, leading to that space. I'm uncomfortable with that line, but you can see how I, there seems to be real tension with these two things I want to say, and I can't say in both. So can you say why there's non-separability in the standard back space by the Haranoff I mean, the fact... It's electromagnetic, isn't it? It's not a problem in that context. Right. Now, and why? You don't want to say that E and B act at a distance. It's local. Right. So you take the A seriously. And so this loop integral, or ring integral of A, the solonomy... That describes a property all or at the loop over which it's defined. And that property doesn't seem to be one property, is all four apples into two points. Simply because the value of that integral is gauge invariant. It is, but I don't think it's simply the point. No, but on the other hand, the value of A at any given point is gauge dependent. Yes, if the value of A at any given point were not gauge dependent, then you'd really have a good thing here. The value of A at each point is determined as a loop integral, and there is only one value of A, because it can be given in a gain-independent manner. But isn't it, well, perhaps you're going to say this is a bad analogy because of the notion of Gage, but take the proposition, I'm writing an article, which we'll say is true of me in a given month.

40:00 I mean, any one of these, whatever you call them, lingering historical or temporally extended whatever predicates, of a whole period in my biography without demanding anything of any single period. In fact, for writing an article, there's very little constraint, actually, on all but a few days of the given month. Since one can write an article in a mulling-over way for 29 days and then quickly, desperately. Now, the thing is that with this loop integral, it's true that you can set A to any value you like such as 0 at any given point or 29 thirtieths of the ring but what choice you make will constrain what choice you make elsewhere in order to make the gauge invariant total value of the ring come out right now that's the same with the writing if I prevaricate for 29 days I've got to write like hell on the 30th but nobody says the truth value of propositions with this kind of temporarily extended predicate doesn't supervene on my minute biography of either the lazy or the diligent author so why why not elaborate separability in such a way that the kind of way in which choose a gauge, but whatever gauge you choose, you'll find linkages between the values of A at different points on the ring, why not say that that's compatible with separability? Just like writing an article is compatible with... No, that is entirely compatible with separability. in two cases of this analysis, because in the case of writing the article, there are all kinds of stuff that we're sticking to the super-genius basis about what was going on within in your environment during that 30-day period, upon which your writing the article, in fact, didn't do it. Whereas in the gauge theory case, the only thing you have to play with is the A. The magnetic field, the field sensor won't do it, A won't do it, and there are no other relevant particular variables just on the supervenous basis. It's the kind of

42:30 the thinness of any potential supervenous basis that's the result in failure of accessibility in that case. Whereas your article writing is still between all kinds of stuff going on. So I'm very confident. I'd like to test your intuition. There is an analog, they've heard of both, In the original Vile theory, the theory of my tool theory, I mean, when Einstein put it at the two clocks, for example, at the start-up secret night, one of them goes to the black man and the fuel, they come together again, they'll be kicking into the ranks. And Lawrence pointed out, the length of the rock would double, depending on its history. Now, you could imagine playing this game, applying this case to a situation where, again, your husband finally had a field set by. You can send these clocks or rods, despite some times around us, because you don't go through. And again, you're going to get an effect, and then sort of an embarrassing effect, seven clocks. Does your intuition tell you that that's any worse than the... The part of the model is that you're showing. The model is how you're going to look at the same thing. Hmm. That's cool. First sight looks like it's the same thing. But you sprang it on me and I might move second sight. What do you think? I'm not sure. Okay. Well, is that a second sight? Having asked the question, you're still not sure. I'm going to have time to wonder at you. I mean I think, I think it's um, I think it's worse because it's um, you couldn't reconcile this with um, you couldn't reconcile this with management. Presumably you don't have to end up in situations where that's perhaps some kind of

45:00 I guess what you need to do, if you're going more closely, is to say something about what the structure of space-time was on the relevant part. It could be flat. Okay. Well, that's simple. It could be flat. The problem is when you start to think about the lasman class itself in terms of the internal structure, That's true. Because that's basically what you're learning. Yes. Right. To be more than an hour or a minute. We don't get to know it. We don't get to know it. But we know enough. One answer might be different, I'm not sure I have to ask you this, but like to watch this, but it might be something to go about. In completely connected elevations I'm really, really all electrons that are charged you would better have the choice of giving rid of the electromagnetic field entirely you certainly don't have to worry about gauge choices or anything like that people would