Particle creation by black holes (contd.)

0:00 His recipe for identifying determinant observables identifies only multiples of the identity as determinant. So it calls the problem back to the more degeneracy for the modal interpretation of ordinary quantum mechanics. the problem that if your density matrix is 1 over n, kind of a projection hypothesis, there's too many things that can be in the spectrum of a solution. And in a way, this problem is worse because the state's pull which comes out trivial, he also shows this in the paper, are dense in a set of states, type 3 von Leibnizmann factor, so they're not rare. The trations that would give problems to the only interpretation of the . So the modal interpretation of Roth's help seems like it's on firmer legs than collapsed interpretations, or the ignorance interpretation, or the ensemble interpretation of mixtures. But it still seems like it's not holding up so well. The model interpretation is initially presented, went hand in hand, with a sort of propositional calculus approach to interpreting quantum mechanics, where one-dimensional projectors correspond to value-attributing propositions, and what we're after is a set of one-dimensional projectors that are akin to truth evaluations. This association looks like it's been broken up here, because we haven't got the one-dimensional projection And of course, by the value to the proposition. So it's hard to know what identifying sense of that is coming in as a little bit of a mouse that doesn't want to say, this observable has this deterrent. My last term is that. So here's a question I get when I talk about It's usually raised by somebody for a white person. I can even think about this stuff when we haven't solved the measurement problem.

2:30 Intrinsically mixed states suggest that there's something misguided in this question. Just suggested that for a significant family of responses to the measurement problem, where intrinsically mixed states turn the responses to nonsense that were severely hamstrung. So two extremes of possibilities. The measurement problem is either much, much harder than we thought already, or it somehow misguided. A typical way of posing the measure of the problem is you wind up with a superposition but you want a mixture. What's the analogous way of posing it in terms of the mixture? You wind up with a mixture but you want a mixture of the sort that you're used to from ordinary climate change, which you can't have. So there's new and interesting things going on. And other things are doing systems. Rob showed us that some of them. Laura for an angelic talk. You have been trained well. Questions? I always find it difficult to figure out whether these results are sort of natural, once you understand all the mathematics, or whether they're really physically weird, as you suggest. So I would like you to find out why following analogy is misleading. If I consider classical probability measure, then it's also the case, well, it's easy to find a sort of probability. Two of them are orthogonal if for any set, one measure will give probability zero to any set which the other measure does not give. Now, if the total probability space is finite, then every mixed measure, not extreme measure,

5:00 is not orthogonal to any pure measure, pure measure, because of course the furniture deltas. But if I go over to a continuous case, say, the interval between 0 and 1, then the pure cases become the Dirac deltas. And it will be the case that any mixed measure, anything defined by a continuous probability density, is going to be a token of, in the sense I just mentioned, to have refuel measure. Now, that would be sort of analogy to the case of your intrinsic mixture. But this is, of course, very trivial. So please point out to me why this is not a good announcement. So why don't people worry about the abnormality in the class of the class? Why do people worry about it? Why don't people worry about it? I don't know. It's just supposed to be an unadaptor. Well, this is just some of the modifications to the mathematics. Why is your worry about the intrinsic mixtape more interesting than what I am saying? And so I'm trying to understand why this case is . We say it's the artifact of the mathematics, with the idea that we could come up with just as good physics and systems than the interest of the biology. Well, perhaps it's wrong to say it's not effective to mathematics, but it's something that comes out in the 20-20 years or 20 years space, instead of profiling. And people, and we go over to the continuous space, people still say, nevertheless, a mixed state defines a

7:30 statistical distribution of pure states, even though the mathematics . I guess what I want to say is, why do they say that? What do you think they could say that? So they're not worried about the same artifacts in the mathematics. In the cases I'm talking about, there's good reason for using the mathematics that makes these possibilities available, reasons how to use it is If you're using a kind of mathematics that makes available surprising things, what are the rules to say what's our method of mathematics, and what is it you need to use it? So I don't know. I don't understand either why you shouldn't be worried in the classical case that you want to set the mixtures or define . The probabilities that define being interpreted is the how it works to be treated from a pure state band or life is OK there, I should feel any better about the . The algebra that we should care about, make these kinds of things available. I don't know how to think about the probabilities assigned by a 10-dividend state in such a way it makes sense to me. We count that non-zero probabilities I'm still learning about it. I'm still learning about it. I'm still learning about it. I'm still learning about it. I'm still learning about it. This is following on a bit in a sense that my question was to ask you for some examples of online algebras which have no minimal projectors. three where they're all in because my vague memory slight study is that you get examples if you take a nested sequence of real intervals all centered on the origin and you so pull them from minus one upon n to one upon n and you look at the l2 space of that well clearly this is an infinite

10:00 space that's a proper subspace in the obvious sense of putting 0 outside it of the L2 of the 1 upon n interval, where n is less than n. Now, I had therefore gathered the impression in chat over the years with people that some of these peculiarities, maybe all of them, depend upon pushing your quantum field theory, right down to arbitrary small spatial scales, and my practicing physicist friends say that's the sort of thing you should be suspicious of in QMT, so I would like to know a bit more about these things are endemic in the physics we must practice, which answers as the skepticism of the practicing guy who says we shouldn't push QFG to small scales. And that's the gospel of the last 30 years where it's thinking about renormalization. I changed the subject to . So I haven't heard this line. I don't see any difference why it worked. I'm wondering, can you dismiss the Thai food back as a lot of . Yes, I didn't know. Maybe it would be in the opposite way. There are no truly . Yeah, we used to say . We've had this conversation before. I mean, something, well, in its 2000s, when it was responding to the proposal, it exploits the fact that you've got to, as I mentioned, you've got to try some space to line the script that was like, it's going to stick to what she's going on and how to do it. It's really important for the genius of the But you can always between each one and each one and the one and the one .

12:30 And that's a bit of a . And . So it's really being courtesoned to appeal to the superset of the other in the Wolverine Center. And then, I'll probably tell you which type one superset of the other in two years. So another thing I would say is, what do you do instead? If you're not going to take one through the series that you're a federal agent, you stop yourself to be a black girl that's highly It's true to just sort of a relational aspect of it. That would have a good interpretation for everyone. Michael, please. Well, actually, my question was more or less Jeremy's, just to make up and make a comment on the previous exchange. I mean, I don't know the answer either, but one suspects pretty strongly that the notion of orthogonality is not analogies. have to do with the possible coexistence of these measures. And that's not the issue. And that's not the issue in your case. All the measures you're talking about quite happily coexist. Yes, but they coexist on this joint supports. Sure. It's zero. Sure. I mean, I don't know that that might point the way towards this analogy, though, because I do think it's quite a different notion of orthogonality. I mean, I think orthogonality, given its association, is probably a pretty dangerous word to use anyway. Yeah, it's always a mysterious thing. Yeah, yeah, I mean... Good question. I accept your point. Gentleman behind Michael. In the face of these intrinsically mixed states, a super desperate adherence interpretation might make the following move. So, fine, the whole state space, by which I mean, the state space that includes all the financial states, is going to be compact, is going to have plenty of extreme states.

15:00 Let's just admit, why not we have these states, as the price we have to pay, to pay even this interpretation. By the way, even in the case of possible probability does this one can cover the sorts of states you can actually justify looking at a suitable boundary So my question to you, Laura, is what's so alt-fire about the kind of activity? What would make that subject a desperate move that we'd best not make? LAURA MURPHY- Why do you call it desperate to be? I mean, that is not a very fair question. Why do you call it desperate to be being with? I suppose it's a deceitism and inspiring to Chuck. LAURA MURPHY- Yeah. Yeah. So it's something that often accompanies culture or retreat to . There is no way to operationalize the difference. It means there are nothing to tell the next days. Well, why would that tell your favorite one and then against the other? Oh, it's, um, so then you can say it's just a metaphorical, bad sense, but not subject to a empirical indication, a commitment to how well to, there's nothing you can do in a lab, but you can tell, it's all in the content of the which is an answer to your question, but even forcing it. I mean, so maybe I just have a metaphysical commitment to it. There's something very nice about probability metrics of this sort. So suppose, yeah, we don't require But still, both in which common, intrinsically mixed omega, OK, well, it can still be a state of Obama etymology. But because intrinsically mixed omega can still be a state,

17:30 albeit not economy, I live on, but because it's not normal, it doesn't have a unique extension Yeah, so we still have a probability. We're admitting it still, but we can't tell the probability is that it's to the projectors of the binomial algebra And end of the question from . Yes, well, actually, at first I should say I'm from Rutgers, but I'm not asking the better questions. Actually, your question was the same as his, in essence, I've sort of a bit of additional motivation. That's to say, in the first place, you said, you were talking about some limitations, but one speaks about the four wheelies of being relative frequencies in some. So relative frequencies is done, so it's sort of motivation. in some way. Secondly, again, I'm one of the . My question, but I think more or less answer to that, was the following thing. I'm not surprised by that it's not unique, because when you drop a kind of volatility, say that you're, what's the motivation for dropping a kind of volatility that you think that can be fair kind of a lottery? Does that uniquely determine all the conditional probabilities? No, it doesn't, because there's many ways of having probability-violating measures that are fair or . You can partition them into infinitely many partitions, and then, depending on how you partition it, you're going to get different . So I'm not surprised that it's not unique. But my question there was, is there a way to use these to sign in a natural way probabilities Do you get the same kind of freedom? Do you just mix it in a sort of nice way to respond to the set of all fair

20:00 I don't know, maybe somebody else. So I think it's useful to get to the point where under pressure from the kind of state we encounter in these settings to realize the kind of state that seems natural and to preserve the possibilities of interpretational moves. So I go out and go out and get access. I mean, and I think the making collaboration with the world actually gave us a new kind of motivation. He wanted to have representations in which we have done to direct out functions. in this Reagan-Hilbert-Space way, and what you can do with the algebraic if you don't have the . Yeah. Well, the states in the representation, the official representation where Right. They're well-behaved there, but they're very well-behaved on any representation Right. It makes sense. So if you want to see . The gentleman with the camera. Your title contained the words Black Holt, and I heard nothing in your talk. Did you not have time to make the comments implied by that? Yeah, there was nothing I had to talk about Black Holt, so that's why I made the video, I apologize. Why was the word in the title? The article was also a joke, not particle. Although, in white hole evaporation, there's some analogy between the thermalization by restriction to the Wachowski wedge and the sea of pocky photons you get in black hole. So there's connections could be drawn. So yeah, I'm sorry. Any more questions? We reconvene in 20 minutes.

22:30 Now, classically, you can't, well, I shouldn't say come, you can't take the strength you can, and exploiting relativistic constraints and exploiting the fineness of the loss of the life. But let's put aside that for the moment, the Visti case, and just consider the situation classically. Classically, if Bob was given sufficient information initially to verify the commitment once he has the key, information about what's in here, which is sufficient for him to perhaps not know with certainty whether the box has zero or one in it, but to be able to tell him that there's zero or one for certain probability. So, cheating here is understood in the following sense. Bob can cheat is he can extract some information from whatever it's given to him, some encrypted bits. He can extract some information about the conviction. So he knows that with some small probability perhaps, it's more likely to be zero or one. And that's on students' cheating because over a series of bit-commission protocols, and you don't want either of these protagonists also want to obtain advantage. Alice can cheat if she can do something which amounts to creating the commitment at will at a later stage or make it more over the certain population. And to say, if at a later stage, the revelation stage, she can convince Bob that she has made the conviction even though she didn't, and she can do that with a 50-30 probability, then she's...

25:00 The question is whether you can do this without either side cheating and you can't classically unless you've explored realistic constraints. And so we can talk about that afterwards. Now, quite mechanically, it was supposed that you could do this by exploiting the ambiguity of the mixtures. See, suppose Alice is supposed to commit to a zero or one, and the protocol is designed as follows. she commits to, if she commits to a zero, she sends Bob a certain mixture. If she commits to one, she sends Bob a certain other mixture of nanoclonal, of states which are nanoclonal to the first mixture. Both those mixtures could be associated with the same density operator. So Bob, in principle, by the laws of quantum mechanics, can't extract any information about which mixture Alice has sent you. But Alice knows, and at the latest stage, she can, at the revelation stage, she can say, I can move to a zero, and then Bob will ask her to tell him precisely which states in that mixture, you know, the Hawaii states, are in what pure states. So here's the mixture, so you'll have a, that's far as, yeah, okay, I have an example on there. So here's analysis, is locked into the commitment. And here's a precise combination of that. Suppose mixture zero is, that is the mixture associated with the zero commitment is 50% spin up in the z-direction, spin down in the z-direction, mixture one, the x-mixture, they're both associated with the same density operator. It looks like Alice Park cheat, because as she supposed at the revelation stage, to tell Bob that for each particle, whether it was prepared in the spin up or down stage in the z-direction, or whether it was spin up or down in the x-direction, And it looks like she's unable to post-hoc, if Bob is holding all the particles, decide on that. In case I haven't made this clear, what else is supposed to do is to send Bob a mixture of particles either up or down in the z-direction or up or down in the s-direction,

27:30 and then he keeps the particles, and so it appears that she has no way of effecting it. But she does, because what she can do is just add an insular, and prepare an EPR state. And here the situation is really very simple, all she has to do is prepare an EPR state, and these states are the same, and they associate it with the X or the Z mixture of Bob's side, so she can steer Bob's particle into either mixture 0 or mixture 1 at world by measuring at the relation stage either in the Z basis or in the X basis. So the commitment stage ends, say on Monday, when Alice says, Okay, I made my commitment since Bob, a mixture, either a mixture zero and a mixture one, so he keeps it. And on Friday, she says, I made my commitment to one, in which case, I guess it was, she has to tell him which product was waste plus or which product was waste minus, and if it was Friday, at least it was a zero commitment, she has to tell him that. But she can tell him that by simply making a mention on her particles on Friday, so on that day she had made no commitment at all. Can I ask, I'm confused about the pop-up, because why did you say that without complaining about it, it looks as if Alice's country? Well, Shikari, Bob couldn't check because the statistics for any right measurement is the same on row of zero and row of one. What does Bob do to confirm Alice's sincerity? Well, when Bobby sent this mixture or this mixture, he's simply holding a mixture which, for him, is essentially the same density operator, so he can do nothing which will distinguish this mixture from this mixture. But if Alice, on Friday, when she's supposed to reveal her commitment, tells him, I committed to zero, then what she has to do is to tell him, give him the following additional information, that on particle number one, I prepared Z up.

30:00 Particle limit 2, what was he up as well? Particle limit 3, he's down, and so on. And then he checks, and he's supposed to... Not very, I mean, every single... The particles are labels. The particles are labels. And they're... That's right. But if she... If she exploits spearing, then there is no way that Bob can tell the difference between Alice sending in an actual mixture, to be honest, or Alice has not prepared any mixture at all. It's a simply prepared EPR state and bottles of history. And then on Friday, so Alice never makes a commitment. It's just that on Friday, she makes a measurement either in the C basis or the X basis and... No, it's cool. Yeah, she has her, she has her on set of particles and so on particles and why would she name it? I mean the particles, she measures the string in the z-direction for the zero commitment and just announces the result, or the opposite result, actually. I mean, she says plus or plus minus. Okay. So Schroding is, let's go back to Schroding's conjecture. This is the way we were looking at it. was that when you have entangled states like that, it really, and for separate systems, it must collapse to one of these two states, so that the competent system is really represented by a mixture, a congress combination of product states. And if that happened, then secure using quantitative techniques, would be possible. Because Alice would have to prepare a specific mixture to correlate with God, and she could not only steer cross particles of wool into any one of the dual-tier intermixtures. So, this was, I mean, this is how theory and practice started messing with trouble, because the way we understood all this was that, look, what Schrodinger has pointed out is that you can do this kind of steering.

32:30 This kind of steering is like the essential quantum mechanical thing that differentiates quantum mechanics from classical mechanics. entanglement and steering are infinitely connected, and Scherner didn't believe that you could do this. And suggested that you could have entangled states, separate systems, and they collapse into these mixtures. And if that was the case, you could do different. So in effect, it seemed just that what Scherner was saying was this. Look, I have no problem with phenomenon, I mean, it's fears. Well, there are two features, in fear and entanglement. You know, in fear is okay for me. That's associated with non-communativity. That's just telling me that particles are wave-like. So in fear is, I mean, I think there are waves there anyway, and there's nothing particularly funny about that. In fear is something we call a disability. And we can understand fears in a specific way. But I don't believe we live in a world in which physical systems exist not locally in entangled states. Because, why not? Well, that would allow Alice to steer Bob's system into any mixture of peer states compatible with his reduced density operator, and I just don't believe that experiments will build us out. He says in the paper, if you do experiments, you can't find it's not the case. In fact, I think that entangled states, which the theory allows, will turn out to be entirely local and so far as they characterize physical systems, that non-local entangled states are just an artifact of a formalism. So, in effect, Schrodinger's conjecture, I mean, the conjecture that if you do the experiments you find that entangled and collapse it this way, raises the possibility of a quantum-like world in which there is interference, but no non-local entanglement. So, this is really the punchline of this part of the tool, anyway. Unconditionistic equipment is impossible for classical systems, only to explore the altruistic constraints, in which the altruism observance of community. What non-commutativity allows are different mixtures that can be associated with the same density operator.

35:00 In fact, in a C-style algebra general framework, as soon as you have non-commutativity, you have ambiguous mixtures. What thwarts the possibility of using the ambiguity of an institute in this way to implement an unconditionally secure victim-written protocol is the existence of non-local entangled states in Allison Barth. So what would allow unconditionally secure victim-written is the absence of physically occupied non-local entangled states. So it seems to us that you could hear Shirley's remarks about the possibility of remote steering as relevant to the question of whether or not security commitment is possible in our world in the quantum sense of good commitment. In effect, you could say that Shirley believes that we live in a quantum-like world where security commitment is impossible. Okay, so that sort of motivates, that was our motivation for the information theory constraints. And the connection between entanglement and victimism. Actually, I gave this talk. It depends where you're coming from. Where do you think that, if you're talking about Einstein, you're talking about relativity, quantum mechanics, making the analogy, and talking about principle theories, and coming up with principles, information theory principles, which characterize quantum mechanics in a similar way to which the logistic principles characterize productivity, depends where you're coming from by what you think is natural. No, I mean, again, he spoke at the first department, or similar to, at UBC, and Bill Underett said that, well, you find the no superluminal constraint, no superluminal transferable iteration constraint very natural, and the non-clinity constraint is very natural, but the non-clinity constraint is very natural, but the non-clinity constraint, that seems kind of weird for a physicist. And I had a tool, a similar tool to a group which this is the most the top of this,

37:30 and somebody in the audience said, well, you know, the non-clinity constraint, that seems very natural, but the non-clinity constraint, that's not natural. So I hope by linking it with steering that it seems so natural. Okay, I wanted to let these two guys now have the significance of all this for interpretive issues. As you see it, okay. So Einstein's claim was relativity as a principle theory. Special relativity, you've got these two principles. Provenance of inertial frames, positive velocity of light. They conflict in Newtonian space-time. So you do revise that to Ninkowski geometry and you get special relativity. And that's the way that Einstein presents it. So we now think of a relativistic theory as a theory for certain symmetry or invariance requirements defined in terms of a group of space-time transformations. And this is through a group of special relativity and a bigger group in the case of general relativity. And we understand this invariance as a consequence of the fact that you live in a world of a certain sort of world in which physical processes are subject to certain constraints. if you're looking at the significance of relativity as a principle theory. Similarly, for Malibu, one theory should be understood as a theory in which the observables and states have a certain characteristic algebraic structure. And just as Einstein's derivation provides an interpretation of relativity theory, a characterization of the conditions under which the theory would be true in terms of certain principles that constrain more like behavior of physical systems, our characterization of quantum theory should be understood as an interpretation in the sense that theory can now be understood as reflecting the constraints imposed on the theoretical representations of physical processes by the information theory of constraints. That's the way we see it. And as I say, now that seems to be somewhat shady because of Rob's result, Rob Specker's result, and that we need also to talk about what we want to say precisely about bid commitment in view of Adrian's secure bid commitment schema.

40:00 Okay, I want to just talk briefly, I don't know, how much time did you say this? Ten minutes to go. Ten minutes, okay, that's fine. I want to talk about these two, which was that there's no deeper constructive theory of quantum phenomena, and that that's excluded by the information theory and constraints. So here's what, here's the museum. It's considered thermodynamics, which is a paradigm example of a principle theory, and a kinetic theory, which is a paradigm example of a structure theory. Uh, Einstein, um, Einstein did a lot of work on, um, Brownian motion, and, uh, he said, he said, according to molecular phonetic theory of heat, rising microscopically visible size, extending a liquid in the Brownian phenomena, with the four movements that subsistently easily observed in a microscope. can actually be observed, then classical thermodynamics, and no longer be looked at as that physical precision of bodies, even of the dimensions, distinguished point of life spectrum, an exact determination of actual atomic, atomic dimensions, and impossible. On the other hand, should the prediction be a direct, a weighty argument to be divided against the military. And Max Bourne says, the fundamental step in mind is that you have reasonably the inferior matter from a possible, plausible, useful hypothesis to a matter of observation, according to cases where you could actually see the stuff. The point I want to make is that at the end of the 19th century, about the existence of atoms. And what seemed to convince them was Poincaré, referring to Perron's experiments based on Einstein's theoretical analysis, said,

42:30 the long-standing mechanistic and atomistic hypotheses have recently taken on enough consistency to see stillness appearing to us as hypothesis. And this is the point. Up to that point, I wanted to find it was reasonable to take them as nearly useful pictures. Things seem to us in favor of stating that we see them since we know how to count them. We know how to count them. And the great determination of the number of admins made, obviously. And I have completed this time with atomism. The atom is now reality. So the model I want to take from this story is just that without the possibility of observable fluctuation phenomena, the molecular-to-date theory would be no more than a physical picture. Well, more precisely why, well, there's a model in X. Why? Because there would then be no critical constraints on the size of the basic building blocks of the constructive theory. Remember, for Einstein, thermodynamics is a principle theory, now it looks like you've got a nice constructive theory with a constructive theory sort of underlying this principle theory, thermodynamics, you've got a kinetic theory, but do we take this seriously, or do we take it really as a useful fiction? well, we should take it seriously if there's some empirical constraint on the scale. The scale of the basic building blocks, right? There's a theory that says, you know, you really have atoms there, so there should be some way to put it down to their size. Otherwise, we could double Abba Dabba's number, and those normal phenomena would remain the same. So, it seems to me that it's reasonable to say that, in that case, you couldn't put a constraint on the size, there would be no good grounds for taking these proposed unobservable aspects of reality seriously as explanations for the observable phenomena. You do have good grounds, though. So we should take it seriously. But what about a constructive theory like Bohmian mechanics? The basic building blocks are Bohmian mechanics,

45:00 of the Bohmian trajectories, and in Bohmian mechanics, a quantum measurement is represented as, it's kind of complicated, a dynamical evolution of the Bohmian particle in configuration space under the influence of the guiding field that's given by the quantum state, which in a measurement process involves in such a way as to entangle position, which is in effect pointer always, and the measured observable. So you get in effect the interfiguration space, entanglement of position, and the way of observable measuring, and the wave function which takes on the form of a batch of humps. And each hump is associated with a certain position. Since the dominant model is at a determinative position, by assumption, this position value is associated with dimension as result. That is, it's associated with one hump in this many-humped wave in configuration space, which is representing the angle of the position of the momentum. So the position is always somewhere, which means it's associated with some hump, and that's correlated with some particular dimension as result. The remaining terms in the inter-angle states can be dropped, because it's the state which is the guiding field which tells you where the particle is going to go, and essentially the particle is going to move or go wherever the wave tells it to go, and so it's in a under one hump. Basically, that's the effective hump, and the other humps far away play no role, play very minimal role in where the Bohr particle would go, so if you have an effect of collapse, you can drop the other two. And that dynamical evolution is explicitly designed to reproduce the Bohr distribution for the quantum mechanical measurement processes. So the positions of the Bohr particle are going to be trajectories, if you like, can never be defined more precisely in the Bohr distribution. Which means that the theory is designed so that there can be no observable fluctuation phenomena, analogous to the observable fluctuation phenomena in the thermodynamics case. So they know empirical scale constraints and the basic building blocks of Bohmian mechanics.

47:30 Now this is scale constraints and it is connected. So the conclusion that here is the opposite of the one with the dynamics theory. There can be no good grounds for taking the unobservable volume trajectory seriously as explanations of the observable point. I guess I'm saying that for a constructive theory, in order to take it seriously, you should have good grounds for taking the unobservable basic building blocks of a constructive theory seriously are empirical phenomena which put constraints on size or scale of those building blocks. So, mobile mechanics is basically a useful picture in Pocahier's sense. Now, other potential candidates for constructive theory of quantum phenomena are mobile interpretations with the same general structure as mobile mechanics. That comes from a theory that Rob and I proved about well, that's how we do patients essentially. So they're all going to have a similar kind of dynamics. They're all going to have a similar feature where they will hide the, where they will prevent any empirical constraints of scale. So it seems to me that in a world characterized by the information theory constraints, part of the mechanics is complete. It's a principle theory in which we can get a constructive theory. And that's the sense, I think, where that, referring to the painting Lord Einstein, it seems to me that complementarity, if you, I don't want to go into Paul, This now is actually before the Driving Act of Complementarity, could be understood as at least consistent with the claim that the information theory really constrains which is too linear as well. That basically is the substance of the tools. I think that's one more transparency.

50:00 Yeah, so it seems, I should say it seems actually, because now seems to be in a situation differently. It seems to us that the way to understand the whole story, then, is summed up in Andrew Steen's quote here. Historically, much fundamental physics has been considered to discover the fundamental particles of nature and equations which describe the emotions and constructive theories. Now here's a different program that needs and important to discover the ways that nature allows and prevents information to be expressed and manipulated, rather than particles to move. So, this was, this is what I think, this is what I sort of think, it ought to be the case about the significance of the mathematical results we proved. But, as I say, it now seems to me that there's a number of worries. The main worry to me, actually, now, because I'm not sure how to understand the significance of this result, is actually Rob Speckin's toy model. The toy model, as I said at the beginning of the talk, has entanglement in it. It has interference in it. So, what do you want to say? I'm not sure what to say, frankly. It might be that the toy model is inconsistent. But I certainly haven't been able to share this inconsistency. It might be that the Tory model, because of the weird constraint and information, actually evades the, does not fall under the class of theories that we consider. I mean, we're considering a very broad class of theories. I should make it clear that in this proof, we assume a lot of connections with mathematical machinery. We assume the mathematical machinery of C-style, because we assume that the dynamics is the most general kind of dynamics that you can have on a C-style algebra, that is, completely positive maps on the algebra.

52:30 And we make certain assumptions about independence of physical systems, otherwise we could be given that one system. So it's possible that the information theory constraints in the toy model actually means that it involves a kind of weird dynamics. because that's playing a role in constrainings and dynamical evolution. Because, by the way, if one considers, when I talk about the most general kind of dynamics, I'm just used to how I wrote, that completely positive maps include zero-three transformations, and it includes collapse transformations on measurement, and it includes anything. So it includes the kind of updating transformations that one does on measurement, but the kind of updating information on measurement constrained by this, well, statement information is really constrained, might actually be very strange and not fall under, I'm not sure about that. On the other hand, in fact, we're the case, one might say, well, there's so much to risk for your sea star and gray clamor, and it's really what's wrong with the theory, like the Tory model. So there are a whole bunch of questions which I have to admit that I'm at a loss of how to answer right now. The other point I wanted to make was that it might just be the case that Schurding was wrong. If Schurding was wrong, then I think I would say that most likely there's a cutting-off war in the paper motivated by thinking about entanglement in a way which was closely related to Trevi's

55:00 thinking in that paper. And it might in fact just be that the notion of entanglement is rather supple. There is entanglement, let me back up a little bit. We do show that from certain information-critic constraints you get entangled. But it doesn't follow from that that the entangled states that you get, which are the sorts of states that are seriously entangled in the sense, Well, we get entangled states precisely in the sense that we get states which are not representable as convex combinations of product states, and that's the usual notion of entanglement. But there's still a question about the old inequalities. I mean, the entangled states in Rob's paper are entangled in the sense that they're not representable that they do not like the balancing equipment. So, it may be that ensuring all the essence of the entanglement, that's not quite right. I mean, it may be that, well, it's part of the essence of the body mechanics, that there's, insofar as you can have entanglements without violating values and equalities, that, um, that the current analysis is fresh for me. So it might be that the, oh, stop the other thing, one more thing, so it might be that the significance of the toy model, which I'm still going to talk about, is that the current analysis was wrong, And if Kerry's analysis was wrong, then I would say that it would be probably a clue if our analysis was real. So I'll just stop there. Let me make a proposal. We're running a little bit late. We're going to reconvene after the coffee break for, you know, I think very leisurely discussion.

57:30 So I suggest that we restrict the questions now. If there are some very short questions of elucidation, now is probably the best one to ask it. We'll sort of... Elucidating question. What's so all-fired and important about information theory? Why an information theoretic constraint rather than a group theoretic constraint, or a topological constraint? What motivates you? Well, I think that the short answer is you. I didn't mean to be that much of one. But in terms of just the psychology of my own thinking, I mean, it could be, of course. I've always been puzzled about quantum mechanics, always been doing something which involves trying to understand quantum mechanics. It was very interesting to me when I heard of this proposal of Yul's and Brassad's that maybe you could get quantum mechanics from cryptographic principles. and it seems weird and outlandish and far out, but when I thought about it in connection with the current originality, which now might be an unfortunate, and in connection with Bohr, who was basically in Einstein, It seems to me that, well, it really might be a very interesting avenue to explore to think that what if we just happen to live in a world in which there are certain constraints on information. Information in the physical sense, by the way. I don't want to model that with knowledge. Information, when I put that information in this paper, the role of information playing in this paper is information in the Shannon sense. And Shannon makes clear that by information, you mean something which involves from meaning, actually.

1:00:00 So, I don't want to make a slide from information to knowledge. So there are certain constraints here. So it seemed to me like a very interesting idea to explore, that we might live in a world which is wired up in some way, where there are constraints on information, and it would be interesting to explore that and see whether one could get quantum mechanics out of that, and then see and kind of rethink what Paul was saying, and say, well, gee, maybe that's sort of what Paul was saying. And then there was the further idea that perhaps what's going on here is that we should think of quantum mechanics as a physical theory of information, for which there's no disruptive theory, and this was essentially Paul's idea. So, it's not, I mean, the answer to why information is perhaps not that deep, but it just seemed like a much, I mean, let me just say one more thing. I always thought that the really interesting thing about the foundations of quantum mechanics was that in fact the only interesting game to play was to try and show how in the face of the measurement problem and weird features of quantum mechanics like all the whole structure of Hilbert's base, to try and show how you could maintain a realist view. And that seemed to me like a very interesting problem. But for some reason or other, I now have switched. I mean, it seems to me that there is much more of an interesting problem. The really interesting problem is to show how you can make sense of war. And that seems much more interesting than how you can make sense of war. Yeah, I think you were next then, Arthur, and then Jeremy, and then I think we'll go this way, I'm sorry. The first theory question, the theory technical question, the C-star algebras that come out of your analysis, what are the constraints on structure of those C-star algebras do you think around the population?

1:02:30 We may not be projecting. We start by just assuming that we're considering a class of theories which can be characterized by having an algebra of observables. So we start with an algebra of observables, which is associated with the C-star algebra. So it's just the general notion of the C-star algebra. So the claim is that we have systems which are associated with observables, which have a certain algebraic structure. The algebraic structure is the most general C-style algebraic structure. Then we impose three formation constraints. Well, I should say we also make certain assumptions about what it means to have two systems. We must say that in the C-style algebraic formulation, we have more than one system, so we must say that we have to have something there which talks about distinct systems, and what we mean by distinct systems. So once we have that, which is sort of very minimal, from a physical point of view, it might be sort of major from a mathematical point of view, then we simply encourage the three information through any constraints. And what that does is to cut out all the classical C-star algorithms. Classical mechanics can be formulated as a C-style algebraic theory, as Fanoi-Mancho, Kurt-Mancho, the classical statistical mechanics. And those theories are commutative, the algebras are observable in the sphere and the community. And there is a representation theorem that you can then represent the algebra on a phase space. And so you can throw away your sister algebra and use physics on phase space. Our information-related constraints essentially exclude all that clause of theories.

1:05:00 My worry is that they don't exclude enough. Actually, we already knew that it doesn't go as far as we want it to go. Because, as I said, we get entanglement and interference, so we prove the classical cases in that sense. But what we don't get, we don't get entanglement interference, which means that you can't represent it in a phase phase. But you can, because this is a fundamental representation from the CISTA algorithm, represent things in the Hilder space. But there are various sorts of Hilder spaces. The Hilder spaces are complex numbers, reals, and so on. And we think our world is characterized by states which are observed in a complex Hilder space, not a real Hilder space. So, we don't exclude the possibility of real opportunity on Hilbert's spaces. Now, I think we should, and it seems to me that that's sort of a further project of trying to figure out what information through any constraint would actually give you complex Hilbert's space. So we have, like, Hilbert's space, as opposed to Fae's space. So it's in that sense that we... I mean, you said, like, what sorts of sea-style algevers we get? we get all the C-style, we get non-communities of C-style algorithms, but not any old non-communities of C-style algorithms, but non-communities of C-style algorithms in which there are non-local entangled states. But we need to get some more, I mean, aside from, we need to get rid, aside from the worry about whether, in what sense, toy models of the spec, which is still in the social media space. The second question is, what is what is important about this? Well, the way I look at this whole project is something like this.

1:07:30 We start off thinking about, well, how are we going to investigate the physical world? Well, it seems to me that we start off with certain instruments, which are black boxes in terms of theory. In fact, much like Lucian's code. So we start off at any point of what we know. I mean, maybe we started with commonsensical mentoring instruments, I mean, sticks or whatever. In the case, you know, if we put it in lots, we started with where we are. So let's say we were in the 19th century, we started with instruments which are classical instruments. And we now, then, we're investigating phenomena with these instruments. And we then perform certain measures, and we have certain information we can get back. And this whole result of our investigation can certainly be formulated in terms of an algebra of observables and states which are understood as expectation values, with the expectation of how to do functionals over observable, any probability measures over these observables. So we don't start off with any sort of phase-based notions or systems which have properties and notions of properties or dynamical variables which are somehow attached to systems. We simply made an investigation with our measuring instruments. And this particular picture is very nicely associated with each of our instruments, that is to say observable, which are pretty theoretical as far as the product is concerned. So we have a theory which we can formulate in terms of our measurements results on our observables, in terms of probability measures over these observables. And then you can ask a further question about the structure of this theory that we did. Okay, now if it happens to be the case that's a certain kind of nice structure to use and so on, we can then, by a representation theorem, represent the whole thing in a phase space, throw away the C-style divide and so on, and apply the phase space representation to everything, including in principle our measuring instruments and ourselves and so on.

1:10:00 them get what Howley called a detached observer description. Howley said Einstein is always looking for these detached observer descriptions that, you know, for you, Bohr, and I know this is impossible. So the possibility of getting a detached observer description that is a face-based description and then applying it to the black box measuring instruments that you started out with really depends on structural features of this C-star algebra of states and circles that you find with your measurements. Now if you can't do this representation as you can't if the structure is such that you have no face-based representation, then it seems to me that you have a situation much like Paul characterized. That is, you can only get rid, ultimately, of the measuring instruments as something outside the theory. Of course you can apply the theory to the measuring instruments to whatever level you want, but because the whole theoretical framework is now a framework of states and observables, where the states are expectations, values, functionals, and probabilities of the observables, ultimately you do not have a decapped observer description. You'll have a description which is a description in terms of observables and what will happen if you perform certain measurements, in which case the observer is not removed from the pages, so you don't have an attached observer description. So it seems to me that the possibility of getting a detached observer description really depends on kind of world hearing. It might be that there are constraints on that, and that when you make an investigation of the world, it turns out that we can't have what would be nice to have, which is a phase-based representation, and we can't have a physics which is in fact observed in physics. And I think that this was the essence of the President. So this is so tied up now in my view of what C-style of our theory is and the role of theory. This first round of questions has gone on already, I think, a little longer than we expected.

1:12:30 So I've got questions in the pipeline, Arthur, Jeremy, and Jos, but let me propose the following. The coffee's also waiting. It's being paid for. It doesn't improve the waiting. And also, we've arranged to make a speech immediately after the break. So, let us have a coffee break, Terry's going to speak, and then I'll resume the question queue where it was and then we can come to the audience. Let's take about ten minutes. So, for example, I've found this system in the algebra of 20. And also, what it is, is that the culture you have to take into account, it's not just the state of OEM, the form of the house, you wanted to choose a specific set of the house, it's very daunting, so you have to say, the theory is restricted to these scenarios, these transformations, these type of user transformations, and this is perhaps different, and then you buy something which is the closed system, I can do the same thing, or if someone says that you did all the pasta, but then you can do the same thing, if someone says that I'm going to make you turn into the trains and to make my class one more time, but then I can find the same number of states in a degree that's not just a number of states in the U.S. Thank you.