 Okay, so let's begin with the second half of the workshop. And we will have the first talk by David Wallace. I thought it was supposed to be on the two part paper, but the title he is from the observability paper, but anyway, he's promising to tell us about his symmetry research in around half an hour. So David, please. Thank you. Yes. And so a curse of the pandemic is it's become almost I mean, relatively minor as curses go. It's been impossible to work out what you've which people have heard which things where. So I've given versions of this material in various places. And I can only apologize to those who've heard fragments of it previously. At least in on the East Coast, it's just after lunch. So if you want to multitask, having heard the talk full with catching up on sleep, I shall not be in the slightest defended and she'll not make any adverse inferences from people doing so. Okay. Symmetry is weirdly more interesting and important in physics and in interpretation of physics than you think. I mean, and you first run into the extent to which physicists care about symmetry when you're an undergrad studying physics or trying to get interested physics on the side, it can seem that people are a little fixated on what looks like a sort of relatively technical work a day concept. And just as a sort of reminder of the focus, I mean, here are nonexhaustedly I think here's a list of observations that are varying made and defended about symmetry by serious people in physics and philosophy. Zoom. There's an unobservability thesis that symmetry related states of affairs are empirically indistinguishable. We saw some of this coming up in Dave's very nice talk earlier. I've got a sense in which if I've got a quantity that if I've got some transformation that takes situation a situation be somehow it's impossible to tell which of situation a or situation b actually it takes. Then there's a representational equivalence thesis if I've got this is more the formal level I've got. I've got a model that supposedly represents some system. And I've got another model I get by applying some symmetry transformation to that system. Somehow those symmetry related models are equally well suited to represent a given physical system. It doesn't there's no fact of the matter as to which of these is the right way to represent system. There's a related but not the same model equivalence thesis, which is more the substantive than the formal level. I've got a state of affairs related to another state of affairs by a symmetry transformation. I haven't really got two states of affairs at all and most I've got a re description of the same state of affairs. And I've got a surplus structure thesis. There's some idea that if there are features of my model that are variant under symmetries and I've got say an absolute space that isn't preserved by the boost symmetries of my theory. The theory is in some sense deficient. How to cash out that deficiency is contested but in some sense then. There's a guide to reformulate in the theory or maybe a guide to which bits of the theory are just descriptive fluff in John Ehrman's trench and turn. In any case the symmetry is supposed to be a guide to which bits of the machinery of the theory aren't doing any work and should be discarded if we can manage to work out how to do it. So that's a lot that we can get from symmetry and the list isn't even exhaustive. And so the office question to ask is why, how does it follow from this relatively technical notion in physics that all of these very substantial interpretive results are supposed to hold. And even to answer that ask that question, we need to get a bit clear on what we even mean by symmetry. And the question about what symmetry is supposed to mean really can't be entirely disconnected from these supposed things we can derive from it. But the notion of symmetry I'm mostly interested in is what's come to be called the dynamical notion of symmetry which is also the notion that Dave was talking about. A dynamical symmetry of a physical theory is a transformation applied to that theory, which takes solutions of the equations of motion to other solutions of the equations of motion. This is now an extremely formal notion. This is a technical thing where you can check if a transformation is a symmetry or not by looking at the dynamics of the theory, very close to the kind of machinery physics side of how these things are done. There seems to be little or nothing interpretation about it. And yet it's claimed varyingly that this dynamical conception of symmetry somehow can underpin all of that sort of interpretation on an epistemic and metaphysical good stuff. And that might be seen as too good to be true if that has widely been claimed to be too good to be true. So you can make this objection at a rather sort of general, how is it possible, you could say and people like does good to have said. This is just a formal dynamical feature of theory. How is it even logically possible that a formal dynamical feature of theory can have substantive implications for our epistemology for our metaphysics for the conceptual interpretation of the thing. Then we have a separation here between the dynamics of a theory and the content of the theory. And isn't it just not on the table for a formal notion like the dynamical conception of symmetry to have these kind of consequences. It's different, I think ultimately more powerful set of objections, which is that, unless we qualify and again this was hinted at at the beginning of those took, unless we qualify the formal definition of symmetry somehow the dynamical definition somehow. We run into dynamical symmetries which clearly can't have these consequences. So the most straightforward example here is just something like my symmetry is arbitrarily is abstractly defined as a transformation that leads the solution to the equation of motion in there and well, take the space of all kinematically possible trajectories through the state space of the theory, consider the subset there that consists of all the dynamically possible trajectories through the state space of the theory. Construct some smooth but otherwise arbitrary permutation on that space of dynamically possible solutions, extend it smoothly but otherwise I'm traveling to all of the kinematically possible solutions and voila dynamical symmetry. And with really very limited constraints coming from differential topology, then this more or less allows you to say that any two states of affairs are symmetry related. And we're not going to be able to get any very substantive interpretation work done from that. And, yeah, that observation has been repeatedly made. You might think that that kind of thing is obviously a philosophy toy nobody in symmetry in physics or both the calling that a symmetry, but there are other examples closer to just things that physicists take seriously that seem to write to rational objections. Gordon Bellert has a lovely paper going through examples of this, and the pick are one of those which again came up briefly when I was responding to Dave. If I look at the central force problem of the motion of the earth around the sun or the moon and the earth, for instance, that theory has that theory obviously doesn't have translational symmetries we've broken them by a choice of center that's innocuous. That's time translation symmetry. That's fine. It has rotational symmetry. That's fine. It's great with all the sort of symmetry related epistemic and metaphysical good stuff looks fine for time translation symmetry. It looks fine for rotational symmetry. There's a thing called the lens ringer symmetry for which it does not look fine. I won't bother giving the technical account of what this symmetry is but it's a dynamical symmetry in the sense that it transforms solutions to solutions. It's a Hamiltonian symmetry. It's actually a consequence of the specific form of the inverse square law. So you see rotational and time translational symmetry in any central force problem, but you only see the lens ringer symmetry when I got an exact inverse square. Transmissions do things like leave the shape of orbits non-invariant. So I can do a lens ringer transformation that takes an orbit that's elliptical to an orbit that's elliptical of a different elliptical shape. And these are relatively clearly things that we don't want to be invariant on the symmetry. So we don't want to come to conclusion that we can't observe those differences or the physical differences at all or the different shaped ellipses are just suited to represent the motion of the Earth around the Sun. You could say similar things about the conformal symmetry in the vacuum sector of electromagnetism. The vacuum EM has the Poincaré symmetries. That sounds fine, but it also has spatially dependent conformal symmetries. Those again don't look like the kind of thing where we want to say they're mere re-descriptions of underlying things that we can't detect on the Earth. Okay, so what do we do in the face of these problems of the dynamical conception? Well, one response is to say that this just demonstrates that this is not the link between the dynamical and the representational and these other features isn't good. There are two authors with very different starting points who broadly reached this conclusion. Here's Gordon Bellott, the ways of encoding the content of laws that are most appealing to mathematicians and physicists appear to lead to notions of dynamical symmetry that are coolly indifferent to considerations of representational equivalents. And here's Shamid Dasgupta, the notion of symmetry is often defined in purely formal mathematical terms so that whether a given transformation is a symmetry of a given set of laws depends just on the formal and mathematical features of those laws and their models. Why should those features of the laws have anything to do with metaphysics of what's real? It's not obvious. And that might suggest moving to a different conception of symmetry and that's a popular move in the literature. So here are the two main classes of alternatively seek. On the epistemic conception of symmetry, which Dasgupta likes, which is Mano Manfrassen like, a symmetry is definitely, whatever else it might be, a transformation which leaves observable features of a theory invariant. Typically, I should say all of these definitions are dynamical symmetry plus, as in it's usually at least necessary that the transformation takes solutions to solutions. But on top of that, we add something else. So on the epistemic conception, we add to the idea that a symmetry leaves the unobservable features, sort of the observable features of a theory invariant. On the representational conception, a symmetry is, in Teralia, a transformation that leaves the representational features of a theory invariant. Usually it does that by being an automorphism of the underlying mathematics. So if anyone who's familiar with the sort of classic space-time tradition of Erwin Friedman, as written up in particular in Erwin's wonderful world, World and Athens space-time, will know that Erwin's conception of a dynamical symmetry is basically what I give. But his concept of space-time symmetry is a diffeomorphism that preserves the absolute structures of the space-time, and then generalizing that outside the space-time context. That's to say it's an automorphism of the underlying mathematical structures. Okay, those alternatives philosophically have a lot going for them. I don't like them, you can say. For two reasons basically. The first problem is that they're boring. The symmetry seems to offer a golden promise that seemed to be able to let us make some substantive, interpretational conclusions about the epistemology of the theory, about the representational functioning of the theory from the existence of symmetry. And the problem from that perspective with these alternatives is they kind of build in the answer. If a symmetry definitionally leaves observable features of a theory invariant, then yes, there is an inference from such-and-such is variant under the action of the symmetry to such-and-such is unobservable. It's short, easy, analytic, and uninformative. I might say that about anything analytic, but this is clearly one of the uninformative ones, even in broader cases. Similarly, if one's really interested in the idea of when symmetry-related situations are representationally equivalent, then it's going to be immediate, but that's the case. If I build the notion of representational equivalence into my theory, but it's equally going to be rather uninteresting. So, you know, the ambitious hope would be to be able to hold on to some notion of symmetry, whereby these inferences carried on being contentful, where the discovery of symmetry allowed us then to make some further inference about epistemology or representational capacity of both, rather than that inference just being part of establishing whether there was a symmetry in the first place. The second concern, and perhaps this is the more serious one, is that there's an issue of naturalism here. If, as is my take on these things at least, one starting point here wants to be something like physics, as we find it, as our guide to how we might think about the structure of the world. If one doesn't want to come in with too many apro-reconceptions but on top of physics, then one needs to worry about the idea that these alternative definitions of symmetry aren't necessarily a good fit to scientific practice, the physics practice in particular. I'm seeing if I had a quote about this, I didn't, we'll come back, I'll just paraphrase. So, if you think about the epistemic conception, for instance, symmetries in the same modern quantum field theory are discovered in a very formal technical sense in regimes which are extremely distant from any consideration of what's epistemically detectable. It's a little subtle on the representational conception of symmetries, but no less true for that. So, while we're used in the mathematical corners of philosophy of physics to the beauty of the differential geometry into the formulation of theories like gauge theories or space time theories in a mathematical language that tends to make the symmetries, indeed, the automorphisms of mathematical structure, generally speaking, that's not the format we originally come across the theory in. And it's usually hard work to discover how to move to the sort of more geometric description of the theory. And our guide to doing so is normally the symmetries. So, the famous example everyone in philosophy of physics knows is the elimination of absolute space, original mathematical structure for space and time, certainly is not invariant under boost shifts. We wanted it to be invariant under boost shifts, so we reformulated why did we want it to be invariant under boost shifts because boost shifts were a symmetry. That reasoning doesn't make sense, except in so far as we have some concept of what a symmetry is that doesn't build in the representation of interpretation. A slightly less well-known example, if you think about electromagnetic gauge theory, the sort of modern fancy way of formulating electromagnetic gauge theory is that an electromagnetic gauge is a connection on a U1 mumble, the gauge transformations there are automorphisms, it's all very beautiful. But of course, the way the theory was initially formulated with a gauge potential is a four vector. And four vectors have tons of gauges on invariant properties. If I want to say this four vector has divergent zero, the property of having divergent zero is in fact it's in naught gauge invariant. Why did we move from four vector formulation to a more austere formulation, because on the four vector formulation, the symmetries were not automorphisms. We wanted them to be, we had a substantive dynamical conception of symmetry and wanted to map that across to the automorphisms. So for these reasons, I badly don't want to give up on the notion of a symmetry as a dynamical concept of theory. Which means I'm interested in trying to see what's the answer to that set of severe problems for the dynamical concept that we came up with previously. And that means, in part, that simply means finding a criterion for which dynamical symmetries are the ones that permit epistemic metaphysical modal inferences. But I don't think it's a good idea just to play that in the sort of the definition and counter example game that we do in philosophy. I don't think we just want to look for a self consistent definition such that it gets all the intuitive plausible cases right. I think we want some understanding of why it is that dynamically the dynamical symmetry that the inferences they have. And that understanding what itself to tell us in which cases it works and which dynamical symmetries don't in fact lead to these consequences. Now I'm going to focus here on the epistemic conception here. And partly for reasons of time, I'm mostly interested in the case of when it is that a symmetry transformation is unobservable or the symmetry related situations can't be distinguished. And here's the basic components of the account that I want to evaluate. And the first is something that came up in the response to Dave Baker and gave correctly identified this as the place in which he's in my in many respects quite similar views come apart. And the first thing I want to be assuming is that our physical theories or at least most of our physical theories are in the business, not of modeling the universe, but of modeling subsystems of a larger system and modeling them under the idealization that they're isolated. So Dave said, in the just in the last talk that, you know, what we're doing in physics at least these days is not working with fundamental theories. We're working with theories that are most approximately true in some regimes and so there's a methodological quest to do philosophy physics, given that situation. And Dave was advocating a strategy of operate under the fictional theory is exactly true work on what you should think then and then make inferences from that what we should actually think. And I want to separate them to two parts. I'm not a fan of that in various respects, but I think, but I think for these purposes in particular, there are two aspects of that sort of pretend the theory is exact that can be brought apart to some extent. I'm going to put aside the question about how whether we should pretend the theory is exact in the sense that we should pretend, you know, it applies on all scales, it doesn't go wrong, especially high energies or this kind of stuff. I'm more interested in the idea that we should pretend the theories exact in the sense that we should pretend describes the entire universe. That cosmological assumption is a really common model move in philosophy physics. But I don't think it's anything very close to what we're doing most of the time in physics. The overwhelming majority of models we consider in physics are not intended as models of the universe. They're intended models a little bit. So if you think just look at the model we run into look at the Earth Moon system. Look at scattering of particles off one another. Look at the one particle sector of a quantum field theory. Look at simple harmonic oscillators. Or just sit back and ask yourself how physics could ever be in the business of saying what we're doing is building theories and impairing the data. If that was always about building a theory of the entire universe. It looks really very clear in physics practice and just in common sense that what we're doing with the overwhelming majority of these theories is taking little chunks of the universe trying to model little chunks hoping we can get away with idealizing the rest of the stuff out of it. And I want to take that as an answer in starting point. I want to say what it is to understand the content for physical theory and so in particular to understand how to think about the symmetries of that physical theory is to understand in the concept that theory is a subsystem of a large universe. That's that one. Step two. Generally speaking what we're doing in modeling measurement of some quantity observation of some quantity in a model is we're trying to understand how that model couples dynamically to another model. So it is possible to do physics in rich enough situations they can model their own mental theory, but it's fairly unusual. Our modeling of the moon system don't typically model the devices we use to detect the motion of the earth. Our modeling of particle physics doesn't normally include the detector. Our modeling of gravity waves doesn't normally include the detector gravity waves. Indeed, in many of these cases it can't include it. It's an interesting aspect of a gravity wave astronomy that the physics of the machine that detects gravity waves is almost entirely disjoint from the the physics of the gravity waves itself. A classical device a classical phenomenon vacuum generally relativity gravity wave detectors are extremely complicated quantum mechanical gadgets and the measurement is being done by some system external to the system we're studying. It might not even be governed by the same detailed physical laws. This incidentally and crucially is the place at which one begins to tease open that question of how a formal property like a symmetry could have implications for an epistemic property, which is the measurements of physical processes. Nonetheless, and the requirement of a measurement is not kind of divine appreciation of the truth that actually requires some kind of gadget that responds differentially to stuff is a lever in which you into which you can kind of throw a crack into which you insert a lever and prize open some space to be able to get a to build a connection between dynamics and epistemology and then up to metaphysics and modernity. But officially, for that to work, the symmetry can't just be a symmetry of the system being measured. It can extend to the combined physics of the system being measured and the system doing the measuring and their coupling. In other words, if I think that generally speaking measurement involves dynamical intervention on my system with another system, then the dynamical systems of the first system in isolation can't in themselves. We can't do anything about the measurement theory, because exit policy, the system is no longer in isolation, it's coupled to something else, and I need to consider the interaction. And so to get constraints on our epistemology from the dynamical symmetries of a system, we have to make some further assumption about whether that symmetry extends to a larger system that includes the measurement. So let me cash out some possibilities there. Suppose we take a physical system, and we couple it to another physical system, what happens to its symmetries? Well, here are three possibilities. The first possibility is that the symmetry of the subsystem is subsystem specific. It doesn't extend to the combined system at all. So for instance, the lender and just symmetry of the central force problem is a specific symmetry to the central force problem. So there's no extension of that symmetry out to some optical device that actually looked at how far away the moon is. Likewise, the conformal symmetry of vacuum electromagnetism is a symmetry of vacuum electromagnetism, the truth that clues in the name. Bring in charge matter, couple it, and vacuum electromagnetism is linear, so bringing in charge matter is basically an option. Now the conformal symmetry in general ceases to this. Clay, if I've got a subsystem specific symmetry, there are no implications for observability because there's no no route by which I can make any inference from the symmetry to how the measurement process occurs because the very fact of making the measurement makes the symmetry cease to apply. And that's a good conclusion, of course, because we didn't want these symmetries to tell us what was observed because they manifestly fail at that. And so we had got a diagnosis of why they fail at that, fail at that because they're not extendable to broader systems than the incubation devices. Second possibility is that the symmetry does extend and extending what I call a subsystem global way, which is to say that I can and I should say throughout this talk for reasons of space I'm going to be a bit loose on technical notions that are rather sharper in the papers on which this talk based. But in the subsystem global case the idea is that the symmetry does extend the combined system. And it extends in such a way that to apply the symmetry I need to do a non trivial transformation of system and measurement device simultaneously. So for instance, in particle numeral to physical mechanics. If I consider coupling some collection of particles to some other collection of particles via some appropriate force then provide the whole system is appropriately well behaved and it's on Galilean space time etc. Then the symmetry of the subsystem it let it be boosts for instance extends to boost symmetry of the combined system, but it does say on the requirement you have to boost the measurement device to I've got a bunch of particles and a device that measures how fast they're going. I could take that combined system and apply a boost and it's still a symmetry of the combined system but I need to boost the measurement device to as a subtle example the engage theory then the gauge transformations that preserve the boundary. And I'm not suggesting that this is a major this is a relatively straightforward proof. It is possible to measure a quantity variant under a subsystem global symmetry so for instance it is perfectly possible in the dynamical coupling sense to measure how fast a particle is going or where the particle is or how rapidly a system is rotating. Measure in the sense that I can couple that system to another system such that different values of the variant property on the measured system. And correspond to different outcomes of the measuring system. However, in those situations it is always possible to reinterpret that process as the measurement of some symmetry and varying relationship between subsystem measurement device. So velocity boost to our dynamical symmetry. If my car is on the highway it is possible to measure its speed in the sense that I can correlate its speed to some just the invariant properties of some measurement device in the sense that were my car moving faster than it is then the measurement device would would record a different number. But it would always be possible to reinterpret that same physical process, not as a measurement of a property of the system, but as a measurement of a relation between the system and the measuring device. So I can certainly interpret my speedometer as measuring the speed of my car. But I can equally well interpret it as measuring the relative speed of my car. There's a certain kind of metaphysical take where I'd say well that the more fundamental property is the relative speed. I'm kind of nervous about that because again I don't like the idea of having to interpret my theories in the first instance as theories of the universe. I want to understand what the properties are of my system. And among those properties are extrinsic properties like how fast is it going. It's still a property, my isolated system, and it's measurable property. But combine the system with another system and now those extrinsic properties kind of pair up and can be understood as characterizing relations between the two subsystems in the larger system. And so on. Third possibility, the symmetry might be subsystem local, which is to say it does extend the combined system, but the extension is trivial on the new system. In other words, there's a symmetry of the combined system plus measurement device, but what that symmetry does the measurement device is leave it alone. Permutation symmetry in particle mechanics is an elementary example of this. If I've got six particles and have the same masses and charges and whatever, there's a permutation symmetry of those particles. If I bring in some more particles, then there's a permutation symmetry of that larger group of particles which consists of leaving the new particles alone and just permuting the old particles. So I can extend the permutation symmetry from the subsystem to a bigger system and the rest of the new bit of the system just doesn't change. Again, the quick comment for those interested in this area. That's in terms of your trivial gauge transformations have that property as well. You can't measure quantities that vary in terms of subsystem local symmetry. You can't measure them even in the sense that you can measure the subsystem global, because you can't measure them at all. There's a subtlety that I'll touch on any briefly, which is in some cases, they get empirical significance indirectly by comparison with the earlier states of the same system. So for instance, there's some empirical significance in the permutation symmetry because you can ask, were the particles permuted relative to where they were earlier? If I have some earlier set of particles and they evolve to some later set of particles, you can ask, well, how does that dynamics differ from what I get if I wanted to evolve to the permuted set of particles? So there are interesting indirect ways that could apply, but I'll mostly leave that out for reasons of today's. Okay, so that's a framework. Let me now return. I've had about 20 minutes. Is that like 25? I should be about finished enough. Okay, I had less time. In that case, there'll be rather less on the isolated systems and symmetries. I had less time than I realized I did. I thought we started at, we were going to start at 10 past, we had to start at quarter past. I thought we had 30, 35 minutes. Oh, I'll take another five minutes. Okay, so does that give us the prospect of having interpretive results and formal assumptions became insane? That's not possible. Well, we can see here it is possible in the sense that what makes it possible is that we have to make assumptions about how symmetry extends from one system to a larger system. And that's not an assumption. That's not a purely formal property of the subsystem symmetries. It's not something, it's something bringing in something extra interpretive. And the thing I want to sort of finish on briefly is the idea that actually there's a broader way in which there's still something formal about a system that can tell us something about the extension of a system symmetry to larger systems. Tell us something defeasibly about it. And that extra thing is that many physical theories we study in physics, including most of those that we slightly complicatedly call fundamental theories, whether that means like Newtonian gravity or field theory or whatever. But not sort of two-body problems or something among the oscillators. Many such theories have a property I call subsystem recursivity. And what I mean by that is a theory is subsystem recursive. If given a certain model of the theory and given an in-practice isolated subsystem of the given model in some sector of the theory, some particular choice of how to use the theory to model a particular situation, then that in-practice isolated subsystem can be represented in idealization by another sector of the same theory. It's easier to illustrate this than to try to give an abstract definition. Suppose I've got a particle theory, and suppose I'm considering a 30-particle system, and they're all interacting under gravity. But 10 of the particles are miles away over here, and the other 20 are miles away over there. So now the interaction between these 10 particles and the 20 particles can be largely neglected. These 10 particles are in practice isolated from the other 10 particles. And there's another model of Newtonian gravity, a 10-particle model of Newtonian gravity, which pretty much models those 10 particles by themselves. The physics of this in-practice isolated subsystem can be represented in the 30-particle sector, can be represented in idealization by the 10-particle sector. And conversely, we can understand any sector as an idealized representation of an isolated subsystem of a different model. So those 30 particles can be understood as 30 in-practice isolated particles in a 100-particle system, where I've got the 10 particles over here, the 20 particles over here, and the other 70 particles way over there at the door. And this kind of subsystem recursivity means, this is very much linked to the idea we should never think of our model as a model in the whole universe, says something like any given model we have can be thought of as an isolated subsystem of a larger model. And for any given model we have, if in fact it breaks down into isolated subsystems, we can think of those as other models. And that gives us some machinery by which we can try to work out what the symmetry extension rules are of a theory. So if you want to know, for instance, in Newtonian gravity, can I extend, I've got a model in Newtonian gravity, can I extend its symmetries and how does that play out? Well, I can understand that, but I think that my model in Newtonian gravity ought to be understandable as a model of a subsystem of a larger model in Newtonian gravity. And then that gives me the resources to say, well, how do the symmetries extend? So the recipe is something like this, you check the extendability of the symmetries of the isolated proper subsystems within the sector. You idealize those proper subsystems as other sectors of theory, and then you read off the interpretation of those sectors of symmetries, and you iterate. I won't give case studies, but just to give people just for time reasons, but just to give people the idea, you play this game in non-multivistic particle mechanics. It returns the idea that the spacetime symmetries are subsystem global. But the permutation symmetries are everything subsystem, I've written this the wrong way now, and actually the permutation symmetries are subsystem local. So there's planes I made in the earlier part of the talk about how spacetime and permutation symmetries work as something which can actually establish once we realize that we can think of isolated subsystems as subsystems of larger isolated subsystems. And we can play similar games with field-threated cases, and I'm happy to discuss any of those in the questions, but the broad shape plays out similarly. We can take a field theory, we can take isolated sectors of the field theory, we can look at how those symmetries extend out from the isolated sectors, and we can use that to make inferences about which quantities are observable within the subsectors. Okay, I think I'm probably out of time at this point, so why don't I end there and leave any of the various loose ends so things we can perhaps talk about in the questions. Thank you very much. Thank you. So as I understood, you mean that subsystemic versatility finds the result of your observability paper. Absolutely, was that a question? Yeah, yeah, it was just before I got to my response, I was just trying to summarize the end of your talk. Do you mean that subsystemic versatility from the two-part paper provides a foundation to the results of your observability paper? I'll just put the papers up here. Yeah, the notion of subsystemic versatility is something I discuss in papers two and three on this list, which sort of take as read the analysis of part one. Okay, so I would call two and three, I call the two-part paper and one I call observability paper. So thank you for the presentation. I will make a response until my 19th and then we'll see. So there was a part of your talk about which I will not tell anything now because I will go into my, I will return to it in my own talk. Okay, so this is the part about whether we should prefer the epistemic definition of symmetry or we should use formal features to derive something logical. Okay, so I will just leave it for a while. I would like to discuss what I have not sent you but which is relevant to your talk. Okay, so you're proposing the observability paper, this classification, this division into subsystem, specific subsystem, global subsystem, local symmetries. Okay, yeah. So, and your, your idea is that this classification which is supposed to be formal allows to infer something about observability. Okay, for me, there is a methodological error here because for me it looks like this three-part classification is itself actually about observation. So it looks like you are trying to derive something about observation from something which is actually also about observation. And so instead of you are explaining by a second thing by a first which is actually of the same kind and which is itself is actually in need of explanation. So now I will try to briefly explain why how it happens. Okay, so beforehand you have this case and Wallis paper of 2014. And there you are speaking about direct empirical status versus its absence. Okay, so a usual Newtonian symmetry is where you transform the whole universe, you boost it for instance, and you do that. And for you, this generates a universal, well, similar to the universal, I call it the universal symmetry. Okay. So for you, the boost of the whole universe is universal symmetry, but the boost of subsystem alone is not a universal symmetry. Because it generates changes which we can observe, if we boost a ship, we observe it from the shore and so on. Okay, so your conceptualization of these examples is in terms of universal symmetry is present versus universal symmetry is absent. Okay, but the same distinction can actually be formulated in terms of in observational terms, because what does it mean to have a symmetry of the whole universe. It means that all the predictions are preserved. That's what I call observationally complete symmetry or you can call it unobservable in your terms. And when you have direct empirical status when you boost just a ship, what does it mean that in your terms you don't have universal symmetry? Well, it just means that you have you not all predictions are preserved. So I call it that observationally incomplete, you would call it observable in those ability paper. Okay, so your distinction between the presence versus absolutely universal symmetry can be formulated as a distinction between universal symmetry, which is observationally complete versus universal symmetry, which is which is observationally incomplete. Okay, so this was about Gryffin Wall's paper, but the same applies to the observability paper. So, you have, you start by saying that when the subsystem is considered by itself, there is no way you can detect the change of the subsystem, but it's not, you are again making the same move as when you were saying that if not all predictions on the universal point of the symmetry is absent. But if we formulate in the previous terms, which I proposed, okay, so there is a solution take within your subsystem, which is alone, you do not add any other subsystem. Okay, so this is the fourth section of your observability paper. Subsystem considered alone. If we transform this whole subsystem, of course, there is nothing external with respect to which this transformation will go. But if you divide your subsystem into parts and you transform one part with respect to another, then you generate a change of observable change of this part with respect to the rest. So within your subsystem, you can have changes by transforming one part with respect to the other. And you will say, well, this is the failure of a symmetry, but I will say it's just observability, it's just observational incompleteness. Okay, and now we get to your case where what you call measurement, where to this first subsystem is added a second. Okay, and then you have three cases. So it's either the symmetry of the first thing is an extendable to the symmetry of first plus second or it's extendable when was it was from the like or it's extendable when I want to transform the non-trivial and the other trivially. So these are subsystem specific global and local cases. So, again, what does it mean that the symmetry is extendable? Well, it means that you transform both in some way and predictions all are unchanged. So this is like what I was calling observationally complete. Oh, this is what in the grips and walls paper you were calling universal symmetry. But what does it mean if your subsystem global symmetry is observable? Well, it means it does not preserve all predictions. Okay, so these are notions of the same kind. The subsystem globality is the preservation of predictions on the whole joint system and the fact that subsystem global symmetry is observable is the non-preservation. So these are notions of the same kind. They are opposite because one is observational completeness, another observational incompleteness, but they are both observational notions. Subsystem globality is observational because it actually means the preservation of all predictions. And what you try to inform from subsystem globality, what you call observability, it's also an observational notion because it's a non-preservation of predictions. So I may be saying again, the option is you are like pretending that subsystem globality is formal and distinct from what you want to infer from it. But actually there's no notions like they are both observational notions if you reformulate them in my terms. And it seems to be a methodological error to try to explain one thing by another thing of the same kind. What we need is an explanation where the cause is different from what we are trying to explain. It should be different in nature. And in any case, it's not what you wanted if you wanted to derive an observational explanation from a formal feature. If I'm right that subsystem globality is not a formal feature then even if we suppose that subsystem globality explains observability of subsystem global symmetry, then you would still be explaining one non-formal notion by another. So I have many other remarks, but let's discuss this one. Great, thank you for those comments. You'll be unsurprised to hear I did agree that there's a methodological error in the argument. I think what's going on with what you're saying is that there's a point where you're deciding to reinterpret my use of the word symmetry according to your own third definition, which is f-semic. And if I was doing that then I agree that the whole argument would be question begging but that's not what I mean by symmetry. So I mean systematically through this collection of papers, symmetry is a dynamical symmetry. So when you say what it means for the transformation of subsystem global is that the transformation leads all the predictions unchanged on the larger system. You can use the word symmetry that way if you want, that's the observational conception of symmetry I discussed, but that's not how I'm using the word symmetry. The question of whether the symmetry is extendable here is a purely formal question about the combined system. I have system plus measurement device. They have a dynamics, which is let it be classical for definiteness, has a self, a Hamiltonian that is the sum of a self-Hamiltonian for system, a self-Hamiltonian for measurement device and a coupling term. And I had a transformation, which in the absence of the coupling term commuted with the action of the self-Hamiltonian. And I want to know whether there is some extension of that transformation to be a transformation on the state space of the combined system such that the action of that transformation commutes with evolution under the coupled Hamiltonian. This is an entirely formal notion. There's no space in that to require that observation is definitional. We can debate what is or is not derived from that formal notion, but it doesn't contain any use of the notion of observations. So I just want to deny that the least predictions unchanged has anything to do with what I mean by subsystem global. I don't think the paper's clear on that. And the other thing I'd say goes back right back to the last moment at the beginning is that it's not quite true that I think extendability, not understanding what I've just said, that I think extendability is a formal notion. Given an actual extension of a system to include a measurement device, it's a formal notion of whether the symmetry extends. But of course, it's not a formal notion of... It's not formally derivable from the system by itself as a sort of fixed model, whether its symmetry extends or does not extend to some larger system. I mean, I've said that there's a surrogate of that you can get in subsystem recursive theories, but it's never going to be a formal property simply upset with the theory. And this is a broader comment. It's good that that's the case because of course there needs to be a certain empirical component as to whether we can detect symmetry transformations or not. I mean, if you take, say, Newtonian mechanical system, is it... That theory has reflections, spatial reflection parity as a dynamical symmetry. Is that symmetry extendable to any device that measures it? And it happens, no, because my device might use the electric field and actually electric physics doesn't have parity symmetries. So actually, it's not true that parity is guaranteed to be unobservable in Newtonian models. Perfectly possible as it happens to determine that the Earth is rotating around the Sun in the preferred direction of rotation established by the differential decay roots of W bosons. But of course, that's not something one could ever have learned from inside Newtonian mechanics. So it's not formal and it's properly not formal. So the other thing I was saying, I'll say briefly, just since you mentioned my joint paper, if you agree, about 10 years ago, that that paper, again, is not using observation as its definition of a symmetry. That paper treats symmetry as primitive and it makes a substantial thesis. It assumes that it's established that symmetry-related situations are unobservable, but that's not the definition of what symmetries are. The paper doesn't engage with the definitions. It just starts with that assumption for global systems and asks what can we do right for local systems. That said, it is true that paper starts with a notion of universal symmetries and tries to specialise the subsystems. I think that's a deficiency of the paper and it's one that I've hoped to remedy in the more recent work. Okay, that's probably all I've got in response. Yeah, thank you. I'm sure you wanted a subsystem global, it's not to be observational. It's just mathematically true that it's not. It's three lines back. Yeah, but the fact that you preserve equations, equations, inter-predictions and so on. Well, sure, indirectly and artificially, but those entailments are not reliably formal features. But I care about the equations. That's the formal level of the theory. Yeah, but all your examples are such that when the symmetry is subsystem global, so when you transform both subsystems and the measurement apparatus alike, they are un-observable. So your typical examples are boost and so on. Even if formally observability is not built in effectively, it's there in your examples. So I'm not going to respond because I think there's a procedural issue here. I think probably it would be sensible for you either to move us into the question session and share that, or if you think the speaker and the respondent should keep you should probably relinquish the chair to somebody else. No, let's continue with other questions. And I will return to my ideas in my talk. So everybody else, if you have questions, why are you always only thinking about transforming subsystem and not about the environment independently? Oh, environment is just another subsystem. If you want to extend it to that, you're welcome. But system plus some environments still isn't the universe. That's still a subsystem, which we should think about in the context of its embedding in larger systems. Yeah, no, independently of what the result is in the universe. I mean, you are concentrating on transforming one subsystem and then you are the other. But how about transforming both of them independently and asking what the seals? Well, if you think you can do that and get some interesting interactive consequences out of it, then go for it. That sounds an interesting project. What I'm interested in is saying, I've got a system. The system has some dynamical symmetries. I would like to know what interpretive consequence we can draw for the interpretation of the system and for the epistemology of the system and for the modal content of the system from those centuries. That's a question referring properties of System X from things System X does. There are then separate relational things we might want to try about how the systems relate to other systems and the symmetry is a rich subject with lots of interesting things we can investigate. Yes, for example, take your subsystem local symmetry, you say that it's unobservable. So it's a symmetry which you apply on the subsystem and then the other subsystem is transformed by identity. And you are saying that in that case, there is no way to get observability. But suppose you have a subsystem global symmetry, but you transform the environment non-trivial, then there will be a difference. There will be observability arising because you transform the environment. You boost the environment, but not the subsystem. So there's a methodological point here. I mean, if I establish a theorem that says in such and such a situation something can't be observed, then if you think that's wrong, I need to know why the theorem is wrong. I mean, one can't simply decide to think of new type of transformations. It's a better case that a given transformation is blocked, but the whole point about proving theorems is one doesn't then have to engage with each of the individual cases. Yeah, I have to say that subsystem global, subsystem local, the observability in both cases is actually the same thing. The observability is the same. If you transform the subsystem and you keep, if you boost the ship, you keep the environment assured, you get observability of subsystem global symmetry. But if the ship transformation is identity, this is the subsystem local symmetry. But you boost the environment, you still get the observability. Why? Because it does not matter where is the environment, where is the subsystem with just sufficient, that one of them will transform. This shows that subsystem global and subsystem local symmetries are equally observable. I don't think I've got anything to say. I didn't say anything. My previous responses. I think it's a question from John. Okay, John. Yeah, thanks. This is, I mean, partially just to make sure I understand the proposal with suffering. Yeah. I mean, so the, you know, the problems that were raised at the beginning of the dynamical approach to it. One of these was there's clear counter examples and some of these were sort of goofy ones, just, you know, scramble things smoothly and some of them were a little bit more physical. And I think I understand in the physical cases how subsystem recursivity is going to solve it. You know, the lens running the case, you're just going to look at two solar systems. You're going to look at whatever you're using to observe the two body problem and then say, ah, well, that's going to get me the sort of eccentricity or whatever that I need. Just because I can't see it clearly enough formally. Is this also going to, is this is this recursivity going to get you around the sort of smooth scrambling silly examples? Or is that? Yeah, I believe so, but it's slightly subtler to establish that the scrambling silly examples are in general time dependent symmetries. And applying the analysis for time dependence symmetries is a bit more delicate because I can't, you know, I can't just think of the symmetry as a transformation on a state space that can use the dynamics anymore. I believe that you could embed the silly examples in that framework and I go through that framework in the first of the three papers in the list here. But I'll confess that I don't have at my fingertips exactly how that specifically going to work here. I think the answer is going to be something like this that. Well, actually, I suppose he's a he's a he's a minimal version of it. Thank you loud. The very, the very idea of defining the symmetry as a permutation of the whole history space is going to make the concept even the concept of extending it to a larger system and there's interactions that this will pin down. So it's one if you think about what extension means for a time independent symmetry, then I'm just saying, okay, I've got a permutation of the state space the system. Well, is there some permutation which commutes with the ICI system dynamics. Can I find a permutation of the state space of the tensor state space of the system bus measurement device, which restricts to a permit to that original permutation and which commutes the dynamics. So if I've already got if I'm if I'm working at the space of whole system histories, it's going to be somewhat subtler even to make that well defined. It's about it can't be done at all that sort of risk to my meal the symmetry is like trivially extendable because it can't be censored. Insofar as it can be defined, I think, although it would be good to check the details that it's going to fall under that general story about time, time dependent symmetries that I tell in the paper but I'm going to make the unsatisputing move saying I have to go back and remind myself of how the technical details go. Sure, sure. But no, that's at least satisfying for you. You're absolutely right that in the circle of better clothes that otherwise it's obviously a hole in the argument. Okay, we have a question by Christian. Okay. Can you hear me right. Yeah. Okay, many thanks David for the talk. We're really, really interesting. It's a very, really a very silly question but some people sometimes distinguish between symmetry of models and symmetry of laws. Now, I want to understand if you're notion of dynamical symmetry, try to identify this distinction or try to replace them by a different distinction. I couldn't see if you're, I mean, which side you are. Yeah, so I'm aligning some details and they're cashed out in detail in the second and third of papers in this series. I mean, so there's several things you could mean so let me have a stab at it and see where we get to. I have in mind something like I have the, I have a theory. And, and then I have sectors of that theory and sectors of the theories are the right things to model specific systems in the world. So again it's easier to illustrate them to be specific about it so my, my theory might be just Newtonian Newtonian gravitational physics, any number of particles any boundary conditions whatever. And my particular sector of theory might be specified by a fixed number of particles and a fixed boundary conditions. So, particular sector of the theory might have two particles and asymptotically flat boundary conditions and be good for describing the earth, moon system or the earth, sun system or something. In fact, you might want to say that a sector of the theory even specified on the mass, excuse me, what masses are. Similarly in field theory, you might say that my theory is just given by the field equations, but my sector of the theory also applies boundary conditions. So, I think symmetries get defined in the first instance of symmetries of the theory, believe the equations of motion theory variant. But then if you ask is the symmetry of the theory a symmetry of a sector of the theory will only preserves the conditions to define the sector so release the boundary conditions invariant in practice. And so, in general, we're not going to get empirical consequences in a direct in people significant sense unless we're looking at symmetries of the of the sector, and not just of the old theory. But even I look at the symmetry of the sector I'm still looking at symmetries of the dynamics, and you want to distinguish that from symmetries of individual models in the sector. So I'm not considering it, for instance, I've got the earth, moon system and I rotate it around the line between earth and moon that's a symmetry and not just of the dynamics but of the specific model. And that's not really something I'm engaging in this this set of work. So, I mean that obviously has interesting consequences with sort of situating the symmetry rating and things but that's a somewhat separate set of issues. So I think the answer to your question is I mostly talk about symmetries of laws. But I'm not. I'm not 100% sure exactly what it was you can you think you're so that's why I've done it with detail about that. Yeah, I'm very do we have time to say something. Yes. Yeah. Okay, okay, yes. I mean, but by symmetries of the law I was referring to this idea that you can map solution into solution and you look at the weather this mapping preserve the structure but you don't care about for example boundary condition or initial condition that you can have in a specific models. So it's like a more. Yeah, structural property of the theories but you are not very engaging in the physical cases in which you're pick some particular boundary condition blah blah blah. So you have this movement right you can have symmetry of the laws but don't know what you cannot have for some symmetry of models or the other way around blah blah blah. I wasn't very clear what you said. Yeah, that makes sense. I mean, there's a place that people talk about symmetries of the laws and similar to the states and I think one piece of physics practice that hasn't had that much attention on the more metaphysical side of the symmetry literature is that there's an intermediate space where we are symmetry leaves the sector invariant if you like, but doesn't leave the doesn't leave the individual states invariant. I think those are actually quite important and a lot of the, a lot of the sort of, for instance, that if you're running notice there and to work out the reserve quantities you definitely need to be running it on a some symmetries of the sector and not just symmetries of all the laws. Okay, thanks. Great. Okay. My last question. Okay. Thank you, David. Very nice talk. I love your papers on symmetries. I have a general question. And very briefly, your argument goes from from formal properties of symmetries and tries to get some some conclusions about conditions on observability of symmetries. I was wondering what you think about trying to reverse the logic of the of the argument, trying to impose starting from some conditions, general conditions on observability and try to get from the argument some formal conditions on symmetries. Have you thought about it? Do you think it's a wood project? Thank you. Yeah, so, I mean, I think there are places where I think that that's viable. I mean, the classic example if you like is Gallaudet's ship. So Galileo didn't have a systematic boost covariant dynamics. What he had was a bunch of observational data that made it compelling the boost for symmetries. By the way, I think this is a really good example of how it's helpful. I think it would be better in most cases to think about symmetries as applied to particular subsystems. Obviously, Galileo had no evidence as what would happen if God put the universe in uniform motion, but he knew what happened on actual ships. And so that's very much a case where we seem to have empirical evidence of boost to symmetries. And so we want to build that into our laws. And you could think later that to some extent, that's the logic of not by 1995 we've got empirical evidence that boosts remain symmetries, even the magnetic sector, how we build that into laws and reconcile it with the source independence tonight. And where I think that project gets off the rails is if one starts bringing in sort of a prioristic ideas as to what's unobservable. I mean, in some sense, observability is always going to be like what do we see? What do we see in the look in the world? What transformations don't really seem to make a difference now? And then how can we boost that up to the level of dynamics? And I think a lot of post-war particle physics you could probably put in this kind of framework. You know, we had a bunch of the fact that the proton and neutron had very similar mass was pretty good evidence for an approximate symmetry of the equations. Because otherwise it would just be a freakish coincidence, you know, nothing mathematically would prevent you just saying what we'll just stipulate if you put the proton and neutron mass almost the same. But that's a pretty weird coincidence. So it becomes pretty plausible that there's some significant understanding of that, you know, the discovery of the sort of the eightfold way families have had wrongs is pretty good evidence for symmetry. So I think that project properly epistemically modestly carried out and based upon context, dependent evidence for specific unobservabilities is extremely important and has played a big role in the way through physics. What I don't think we can do is suppose that we know what's observable and what isn't by the natural light and then build a physics around it. We've tried those points we got learned. I mean, parity is the classic example. Thank you. Okay. I'm satisfied with the discussion then we have seniors there. Okay. If you could stop Sharon, I would. Oh, I'm sorry. Let me break out a bit. I'm sorry, I didn't catch your request. Okay. Okay. Yes, thank you for the talk and for saying.