Opening remarks / Christopher A Fuchs: QM as quantum information (& others) (contd.)

0:00 ...everything just on observable magnitude. Einstein's reply is very interesting. Possibly I did use this kind of reasoning in 1905, but it is nonsense all the same. It may be, as Einstein makes a long discussion about his view of... How measurements really work. But there's this key paragraph here. He says, it may be heuristically useful to keep in mind what one has actually observed, but on principle it is quite wrong to try founding a theory on observable magnitudes alone. And here this sentence seems to be very important. In reality, the very opposite happens. It is the theory which decides what we can observe. Now, unfortunately, in the 1920s, Bohr, Heisenberg, Pauli, and others took the 1905 approach as a model of a supposedly operational physics. Now, the later Einstein is saying that, well, the 1905 approach is strictly speaking inconsistent, and I agree with that. This is certainly the most common point of view is that the view introduced essentially by Minkowski in the modern perspective you would say, well, you have particles and fields on Minkowski spacetime and as in Einstein 1926, you use the theory to figure out the behavior of real rods and clocks. Real rods and clocks are not some theoretically self-sufficient things. They're filled out of atoms obeying these dynamical laws you've written down. And actually, there was just a peculiar thing in the 1950s, a physicist called Terrell calculated what a small rod is the limit of a small rod, what it would look like. Now, relative to a moving observer, what it would actually look like, taking into account optical effects, using, of course, the objective realist physics of Minkowski's space-time, and he figured out that the optical effects actually cancel the Lorentz contraction in the limit of small rods. And so what you would actually see would not be a contracted rod. So this to me is an example of Einstein's point 926. You use the theory to figure out what is really going on and how to observe things and what your observations mean.

2:30 And to have such a theory, you need a theory that tells you about the world and how it works. The world being all things, whether you call them systems, apparatus, equipment, people, light beams, optic nerves, whatever. Similarly, clocks, I mean, you would use these dynamics to calculate the effect of acceleration on a real clock and use that theory to design more robust clocks and so on. Okay, even human beings, I would expect, maybe not everyone would agree, but human beings in a spaceship at high speed with respect to the Earth, even their thought processes as well as their heartbeats. I would say art will be slowed down with respect to us. It's not going to be that the observer in the spaceship is timing his own pulse and he's counting mentally and he's going to notice his pulse is really slowing down. No, no, no, his thoughts, I would expect that. So now, in the modern view, when I say modern view, I mean the point of view of high energy particle physics and field theory. What is the key principle of special relativity? The Lagrangian density is a Lorentz scale. That is the key point. All this business about... Classical light waves always moving at speed C seems to be not really the fundamental point in a modern point of view. Think about, for instance, electroweak theory. Fundamentally, you have four massless fields associated with W, Z, North bosons, an electromagnetic field. After spontaneous symmetry grazing, three of them become effectively massive. The electromagnetic field, because of some quirk of the theory, happens to remain massless. It doesn't seem that the fact that photons don't have a mass, well, let's say it turned out in the future that they do have a small mass, no one is going to rewrite special relativity just on that basis. So photons play no fundamental role in defining the structure of space and time. Okay, so we first discovered Lorentz invariants via the classical electromagnetic field.

5:00 But this is just a historical accident. The speed of classical light waves plays no fundamental role in modern high-energy physics. Indeed, classical light waves don't play a fundamental role. Einstein's 1905 paper, I would say it's a historical heuristic only, and that Einstein later recognized as fundamentally consistent. And I would also like to mention It seems to me in some of these discussions, there creeps into the background a sort of implicit assumption that if you have some very simple principles, And if these principles are universal, in the sense you can apply them to any system, it doesn't matter what it's made of, how you prepared it, that this somehow means that these principles are fundamental. Now, the experience of physics shows us that they're not necessarily the case. For instance, Newtonian mechanics, three simple laws of motion, apply to everything, specks of dust, planets, rocks, the moon. Now we would say it emerges in a complicated way from quantum field theory, low energies, classical limits, and so on. So simplicity and universality does not imply it's fundamental. Of course, perhaps even special relativity itself, as a number of people are thinking these days, might just be something that merges with low energy. Maybe it does, maybe it doesn't. Anyway, my point here is that Einstein 1905 is not an ideal model for fundamental physics. That will be relevant, I hope, later in the talk, so I'm going to have to go very quickly and just mention, so now just sketch a little bit of background, a realist view of quantum theory, certainly not the realist view, there are other possibilities, but it seems to me a reasonable candidate. So, pilot wave dynamics of the Freudian boom. It's just based on two simple equations, the Schrodinger equation and a guidance equation for the velocity of a configuration which basically follows the wave crest in configuration space of the wave function, J is usually called the quantum curve. None of this is terribly important. The details are important here. One point that's important is that in this theory, if you're given an initial distribution of configurations,

7:30 So, if you have a function that is equal to the modulus squared of the initial wave function, then you recover the born statistics for quantum experiments at all times t, shown by Bohm in 52. Now, where does that distribution come from? Well, you can account for that distribution as an equilibrium distribution analogous to thermal equilibrium in classical physics. There are arguments that a coarse-graining H theorem analogous to the classical one, and bear in mind that in this picture we know for a fact that every system we see has had a long and violent astrophysical history going back to the Big Bang. So there's plenty of violence in the past in order for relaxation to occur. A numerical simulation for a very simple system, just of particles in a two-dimensional box, we started out with a wave function that is a superposition of the first 16 modes. So, psi squared is shown at the bottom, and we started out with a distribution of particles that is not psi squared, and we let the particles evolve according to the de Broglie bone velocities. And this is a periodic system after a certain time, 4 pi in our units. Psi squared recurs to its initial value. What happens to P? This is what happens to P. And we've coarse-grained P over some very small cells here. So this is a very, quite a simple system. And you see this very efficient relaxation to equilibrium. Certainly one would expect the violence of the early universe and so on. One would expect, in this theory, that when you look around, you're going to see the born wrong. Nevertheless, in this theory, non-equilibrium can exist in principle, perhaps in the early universe, maybe. Simple point is that in a deterministic theory like this, the initial conditions are conceptually independent of the dynamical laws. So, for example, if I had this situation, a simple diffraction experiment, in Bohm theory, if all the particles happened to start out above that red dotted line,

10:00 they would all land at the top half of the screen and you'd only see one half of the diffraction pattern. Let me talk a little bit about properties of non-equilibrium. Generically, in non-equilibrium, you get this kind of thing. First of all, you do, so fundamentally it's a non-local theory, as you'd expect in a hidden variables theory. You find that in non-equilibrium, even at the statistical level, you get instantaneous signals in entangled systems. You do something here, the marginal distribution here does shift. You also find contextual statistics for quantum experiments. So, for example, in an EPR setup, which you can sort of think of as a contextuality of the distance, so the statistics here depends on what direction I measure the spin over there. Cloning of quantum states, sorry this is all very sketchy, this sort of background, cloning of quantum states, basically if I have two wave functions that are not orthogonal, the de Broglie-Bohm trajectories associated with those two wave functions tend, are generally different. Now, it turns out that out of equilibrium you can access more detailed information about the trajectories than you would be allowed to in quantum theory. So, you can figure out which of the two wave functions is guiding the particle, and then once you've done that, of course, then you can just... Do a preparation that creates the wave function you want to copy. Another point is, which I'll come back to later, but let me mention, is non-additive expectations to incompatible quantum experiments. Non-commuting quantum observables, the expectation values are not necessarily additive, but I'll come back to that. And here I'm just finishing up the background, and I think I'm almost a little bit later than I thought, but anyway, I should mention that all this talk can be, I've talked about de Broglie-Bohm as an example, it can be generalized to any deterministic hidden variables theory. Let me just sketch something simple.

12:30 Here, let's just take a single qubit or spin-half particle. I'm measuring its spin along a certain axis that I can choose. That's my measurement setting. The outcomes are plus or minus one. There's this quantum observable. Now, in a deterministic theory, the outcomes are determined. There's some function that maps from the measurement setting, the hidden variables, to the outcome. For this theory to reproduce part of the statistics of quantum theory, there has to exist some distribution of lambdas when I consider an ensemble, such that the expectation values of this outcome match the quantum distribution. There are such theories. For example, one could hook up other theories. The point is, once you've got any such theory, the theory consists of two parts. There's a deterministic mapping from the hidden variable to the outcome, and then there's a probability distribution over the hidden variables that then gives you the statistics of outcomes. Now, if I keep the same mapping from lambda to outcomes, I can fiddle with the distribution of lambdas. Why not? In principle, I could just consider, now once I've got this theory, I can consider an arbitrary distribution of numbers, and of course, in general, the expectation values are no longer going to be the same as what they were, and the Born rule will be violated, so here's a simple sketch here, so say in a two-outcome experiment, there's a partitioning of the set of hidden variables that goes to plus one over minus one, now... With a certain measure on this set, I get the quantum statistics. In general, with a different measure on this set, I get the different quantum statistics. Simple. Okay. Now, so there's the background. So now, how much time do I have? Just under 30 seconds. Okay. Okay. So maybe I won't have time for hard... Okay. So with that background... Clifton, Boob and Halvorson. So, they assume statistical locality and no cloning.

15:00 These are both violated in quantum non-equilibrium. I'm just going to make some statements and I'll discuss a bit later what's the significance of this. But these are facts, unit deterministic and variables theory. In equilibrium, these are violated. Now, Timson has made this point. To me, last summer, I think it was, well, they're also assuming expectation additivity to outcomes of quantum experiments. Now, we know from Bell, 1966, that from a hidden variables point of view, expectation additivity is very remarkable. And it's violated in non-equilibrium for all deterministic hidden variables theories that we model. I'm going to come back to this slide. So why is expectation additivity remarkable? Well, think about again that single spin. If I've got a unit axis, some linear combination of two orthogonal axes with the coefficients, the product, the non-zero. So it's a fact that the, that the, so basically the outcome of a spin measurement along any axis is always plus or minus one, so they're not linearly related, okay, this outcome along this axis can't be, let's say, sorry, the outcome along this axis can't be linearly related to outcomes along these axes, okay, because there would be a root two, for instance, that's 45 degrees, this is Bell 966, these are unequal for every value of lambda. Every value of lambda there, unequal. Now, there is a certain distribution, the one that gives you quantum theory, such that when you average both sides, they become equal. Now that is a kind of miracle. It's certainly specific to this particular distribution. In general, these are unequal for every lambda. Well, if I average over some arbitrary distribution, they're going to remain unequal. So this order result, this additive expectation, is a peculiarity of this special distribution. That's hidden variables theory. So the other thing I'd like to mention, and it seems to me that this point has somehow got lost in the literature,

17:30 but expectation additivity is also very powerful. So powerful, in fact, that it implies the full rule. So on here, I'm just going to show you, this I've taken from... While von Neumann in 1932 effectively proved this, but it's a complicated proof, much simpler proof by Albertson in 1961, I've got this from Ballantyne's Review of Modern Physics, 1970. I'm not going to go through it, I'm just going to put it on the project and take it away, just to show you that it's just a few lines. Okay, the point I want to make is that there's a simple proof, there's just a few lines, arbitrary emission operator... You write it in this form by introducing these new emission operators, you fiddle around, you use expectation and activity, and you find that if you define this thing here, you get that you've got the whole rule, okay, and it's just a few lines. That is the whole proof right there. So... Expectation additivity is very, very powerful, implies the Bourne rule, so I think Timpson in his thesis is right to suggest that the C-star algebra with linear expectation functionals may be doing much more work than one might think. Now, I think one has to go through this and figure out a bit more clearly what is going on, but certainly I think this is a concern. So from the point of view, certainly from the point of view of hidden variables, these axioms and constraints merely capture some key features of an equilibrium phenomenology just as thermodynamics does for thermal systems. Now I'd like to complain a little bit. The analogy with special relativity in the Clifton, Booth, Alderson and in Booth's later papers, this analogy seems to me very incorrect. The analogy they draw is the following, that the Minkowski formulation is supposed to be analogous to standard Hilbert space quantum theory, and that Einstein 1905 is analogous to their axioms. Now, the problem I have with this is that the first analogy seems to me wrong, because Minkowski gives a constructive theory of the equipment, standard quantum theory does not.

20:00 If you looked at standard Hilbert space bottom theory and you, say, took an Everett view, then I think one can say, yes, that would then be analogous to an Enkhovsky formulation, but I think that is simply a wrong analogy. The second analogy I agree with, and I would add that in both cases, Einstein 1905 and his axioms, it's not a fundamental or complete or strictly consistent. There are many reasons why you're not given an account of doing physics, because you're not given an account of the equivalent kind of reasons I said about Einstein 1905. It's a heuristic and phenomenological point of view. I should mention, and it seems to me, that I think the Einstein 1905 paper is responsible for a lot of misleading. ...things in physics in the 20th century. I have to complain about this point. CBH say that space-time symmetry is a consequence of the operational behavior of macroscopic rods and clocks. It seems to me that there you're ignoring a century of high-energy particle physics. I don't think any particle physicist would take that view these days. He wouldn't, when he, I don't know... Calculating the decay of a muon, and he uses the Lorentz transformation to go to the rest frame, he doesn't say, well, I use this Lorentz transformation because the photon is massive, or because of the behavior of macroscopic rods and clocks. No, he can't look at the basic theory that I believe, the gradient density of the Lorentz scalar, and so on and so on. This statement in wider quantity seems that Jeff is sort of maybe moved on a bit from this point of view, but let me just comment on the paper of wider quantum. This statement, our measuring instruments ultimately remain black boxes at some level. Well, standard objections, who is we? Microscopic, little insect, microscopic person, advanced human being from another much more advanced civilization. Who is we, which instruments, at what level. Then there is the argument which I'm here too, maybe I shouldn't go on too much about this, because it may be just not so firm on this anymore, but it seems to, so let me just make some statements.

22:30 Okay, it is a fact that the details of the de Broglie bone trajectories are hidden in this equilibrium state, but nevertheless it gives you a coherent theory of micro and macro, whether it's the right theory I don't know, but it is a coherent theory. I don't see the CBH approach so far as being coherent any more than Einstein 1905. The Breuil-Bohm theory predicts the Born Rule to high accuracy in our world. We know that our world emerged from a hot big bang, so we're not putting it in by hand. It's explained by the early violence. Here, a tricky point, in my view, and other people who work on Breuil-Bohm disagree, If you believe Breuil-Bohm or indeed any deterministic hidden variables theory, it's scientifically rational to expect the existence of non-equilibrium somewhere, whether in the early universe, there's some recent speculations about black holes. I put rational in quotes because It's not clear that there really are definite principles in scientific reasoning that one can really point to and say this is the subject. My feeling is that if you believe this theory, then you should be out looking for non-equilibrium, and that's what I've been doing for some years now. And if you find it, there will be violations of these constraints. If equilibrium turned out to be exact always and everywhere, what would one do? I think I would consider other realist theories. In the meantime, clearly, the evidence is not a determination here. I could cook up other theories with different trajectories and still give me quantum theory and equilibrium. I agree with Jeff, we should suspend judgment, but I would say we should, while we do that, we should consider all the consistent theories too. Some of the arguments in the book, why the quantum seems to me a bit, clearly non-equilibrium is excluded if you assume quantum theory is true, but let's be careful not to argue that if quantum theory is true, then quantum theory is true. Some of the papers, it seems to me there's a sort of shift.

25:00 From suspending judgment to claiming that these theories are impossible, but perhaps we can discuss that. The idea that information is not a new sort of physical entity, okay, I think... Okay, so basically I think perhaps Chris Simpson is saying something like this. We all agree that pointer configurations are real. You can apply information theory to their statistics. It seems to me that the words information is real doesn't add anything to what has already been said, that there are pointer readings. And their statistics have certain mathematical properties. We all agree on that. This information is real. It seems to me you're not actually saying anything substantive. Then I have to also complain here about the sort of, in the paper, why the quantum is kind of a folklore link between special relativity and the idea that fields are primitive entities. Look, I can have a non-relativistic theory with primitive fields. I can have a relativistic ether. So I don't, I just don't, I think that argument is again stemming from some historical unfortunate baggage from the 1905 paper. Let me skip Hardy and let me skip the comparison with thermodynamics and let me use remaining time to comment on Fuchs. Particularly Fuchs, but a paper by Taves, Fuchs, and Schacht, which then just has to be pointed out that there's something wrong here. Quantum probabilities and Bayesian probabilities. In the abstract, it says, we show that any Bayesian probability assignment in quantum mechanics must have the form of the quantum probability rule. Now, they explicitly assume, with no justification, non-contextuality, we know that by itself this implies the Born rule, that it's unnatural, of course, in a contextual hidden variables theory. So now, but yet, there is a claim in this paper that Gleason's theorem can be regarded as the greatest triumph of Bayesian reasoning. But Bayesian reasoning played no role in obtaining the Born rule. It seems to me there's an analogy here with Jaynes' work in classical statistical mechanics, which this paper cites as an example of the success of the Bayesian approach.

27:30 It's well known that Jaynes makes assumptions that amount to assuming what should be proved, assumptions like the uniform prior on phase space. I think there's a similar issue with this paper. Do I have time? So, okay, so now I'd like to make a few comments on Fuchs' paper, this, what seems to be the key paper, Quantum Mechanics and Quantum Information, and only a little more. So, clearly, as Chris has said, this is a changing and developing perspective. It doesn't have a definitive viewpoint yet, fair enough. What seems to be the key idea is that one should factor, look at quantum theory, factor out the subjective elements, and you're left with the objective elements, perfectly reasonable idea, and my suspicion is that you're going to end up doing that, you're going to end up moving towards hidden variables, which is what rocks beckons. That's how Ross Beckens has ended up, but we'll see. But anyway, what I wanted to take issue with is not that idea, which is fine, but I disagree with some of the arguments that have been given. In one particular point, this claim that size, pure state, the wave function is a state of knowledge, this idea of Einstein and Ballantyne, it might be true. I've already mentioned Nelson's theory, if it really is a consistent theory, but I disagree with the argument for this. So the argument that Fuchs presents is based on the old business about from locality. The argument from locality to an epistemic wave function considering two entangled systems, here's a quote, the most powerful argument for the quantum state subjectivity now follows. Since we can toggle the quantum state from a distance, so the measurements I make here, you get this, I can steer the state over there, it must not be something sitting over there, but rather something sitting over here. It can only be our information about the faraway system.

30:00 Now, the problem with that, leaving ever a sign, is that locality is inconsistent with quantum correlations. Locality, via the EPR argument, implies that distant outcomes are determined in advance. Okay, because if I make a measurement here along the same axis as the measurement being made over there, I can predict with certainty the outcome. Now, if you assume locality, that means, well, whatever I do over here, that is still determined in advance by something. And derive a Bell inequality violated by quantum theory. Now, this first part of this argument is something that unfortunately still many people don't appreciate. Bell, with some frustration in his book, puts it, it is important to note that determinism, this is in the ideal case of perfect correlation, perfect measurement, it is important to note that determinism in the EPR argument is not assumed but inferred. It is remarkably difficult to get this point across. Once you've inferred that, you can run the dull argument. So what I want to say is that the starting assumption here of locality actually contradicts quantum theory, so to use locality as a starting point to argue that, look, this state vector is epistemic, the conclusion might be correct, but I think that the argument doesn't stand up. Another thing I'd like to comment on... There's an argument in that paper for non-contextual statistics. The argument seems to be something like this, that if an agent makes the same Bayesian probability assignments for what appear to be macroscopically distinct experiments, then it makes sense to identify those experiments. They are the same measurement. Now, by this point of view, and here's a quote, non-contextuality is a tautology. It is built in from the start. Asking why we have it is a waste of time. Now, but here's something. So, let's think of an example, a simple example of non-contextual statistics, the old EPR thing, where the statistics here don't depend on which commuting observable I measure over here.

32:30 We've just said that if you assume locality, if you assume that the outcome over there does not depend on what I'm doing over here, you contradict quantum theory. So each outcome is contextual. So now here's the point. Well, if you're saying that these measurements... This is A and B. These measurements and these measurements are the same measurement here. If you're saying that that is tautologically the same measurement over here, well then why are the individual outcomes here not the same? Why do you only get a statistical non-contextuality? So in this EPR case, noncontextuality is locality, at least for these measurements we're considering. So the former principle of locality that was used to argue for an epistemic psi is that now merely a tautology. It seems to me that there's some problematic here. I would rather take the view that statistical noncontextuality locality is empirical. Like Lorentz and Behrends, it's empirical. You can't just derive it just by thinking about thinking or by thinking about how to think about measurements. It's an empirical fact. One might accept it as fundamental. Maybe it is fundamental. It might be in a stochastic hidden variables theory. I don't think it is in a deterministic hidden variables theory. It might break down in the future, again like Lorentz and Behrends. And I think I'm about to wrap up. I'd just like to maybe, if I have time, do I have two minutes? Okay, so let me wrap up and say, concluding remarks, general remarks, I think from any realist perspective, including my friends, whoever, that these axioms, the Boo and also the Hardy, that I didn't have time to discuss, I don't think they solve or even address the measurement problem because I have this thing with macroscopic equivalents on our fundamental. It seems to me that Fuchs does not want to go in that direction. He wants to more take the step of going to the Minkowski, from Einstein 1905 to Minkowski, what one would end up with, whether it's hidden variables or Everett or whatever, would be interesting to see.

35:00 So that is not Andrew Fuchs, but certainly Hardy and Tristan Rubin-Homerson. I don't think it solves or even addresses the measurement problem. Also, it doesn't prove or even indicate that quantum theory is fundamental when one thinks of it. Parallel historical examples, specific criticisms, while there are non-equilibrium counter examples, some of the reasonable assumptions that you make are in fact not reasonable from a hidden variables perspective. And my suggested way forward is rather the further development and tests of realist theories, whether it's relational or whether it's... Looking at what you end up when you factor out all of what you think is subjective and important theory, whether it's new kinds of hidden variables theory, that to me is the way forward. Thank you. So, as an Einstein editor, I just wanted to make a few quick footnotes to all this Einstein analogy that is bandied about. So, first of all, this important view, this important issue about instruments as black boxes, right? And Einstein moving from clocks and rods being primitive to clocks and rods should come out as solutions. That came out of this discussion with Herman Weil over his gauge theory, where the line element is no longer directly observable. And then Biles' comeback is like, look, it shouldn't be, it should come out. Now, the more important point is about principle and constructive theories. So, I agree with your criticism of principle theory. Einstein, of course, both in the 1919 article when he introduces it and in an earlier letter in 1908, to Somerville, strongly prefers constructive theories. Now, the irony is, once he started to do that, when he started to work on it, He never produced anything useful ever again, right? So what he was doing with his principal theories, and there I think the spirit in which Chris Brooks used the analogy is actually right on the money. It's not sort of the finished theory you should look at and re-indicate it yourself. It's a heuristic, right? And it's exactly that sort of way of pulling out the empirical generalizations that

37:30 I just want to guide you forward, and I'm not just doing this for special relativity, this is also the methodology you follow, so it's always important to work on quantum theory, so I think if you view the project of Chris and Jeff Hoop from that perspective as like a heuristic rather than as a characterization of Finnish theory, then it comes out looking much more reasonable. I agree completely. There was a suggestion from your talk that C-style algebra makes a linearity, an additivity assumption, as you put it, which somehow seems to exclude Bohm's theory or is unfair to Bohm's theory. I don't know whether this was clear from your talk, but it's not the case, of course, that bones in the... And then you have to tell a measurement story, just as Bowe does, which connects the theory of this commutative c-style. I think I can clarify. So, certainly, within the Broy-Bohm theory, if you allow the possibility of non-equilibrium, then you have new kinds of measurements that are not possible in quantum theory. You would be able to measure trajectories and so on. And then things from a sort of broad conceptual point of view would be more like classical mechanics. And yes, you would have in what you call sort of face-to-face representation, something like that. And you could encompass it in the C star algebra. We're just restricting ourselves to quantum experiments. We're not going to say, oh, here I've got some non-equilibrium matter, do a sub-quantum measurement. No, no, no. I'm going to do the usual kind of operations, fire a carpet into a stern go-lamp, for instance. So use the usual quantum experiments. And the only thing I change is I say, well, let's imagine that the initial distribution of hidden variables is non-standard. All of these will disagree with quantum theory and you get things like failure of additive expectations, so presumably the issue would really be that with the C star algebra, if you have some other assumptions that are forcing you to consider quantum life experiments in your case, then the C star algebra is going to immediately give you the wrong rule.

40:00 Today what we'll do is we'll put the speakers up here first of all, then Ari's going to fire things off and then we can make up for one or two to sort of let loose. Okay? So this comes down here. We can sort of sit here like it was a book. I guess I'll get things going. So, my question is to Jeff, and it's related to the spirit of why this session was organized. Why quantum information? Is it the way forward? So, you're at a constraint. I keep hearing, well, this gives us entanglement, this gives us non-commutativity, things like this. It seems like to... Explain why you assume the inclination period of axioms or microscopes or whatever you want to call them. You go to physics. So the worry is, well, why are you going to information at all? It seems like just a nice way of re-describing the physics, which is your central motivation for making these assumptions. Why bother with information talk? And then why talk about... You know, measurement instruments such as black boxes. I'm still having trouble with why the move to relational quantum mechanics. That seems to be getting us even further away from an information theoretic perspective on quantum theory.

42:30 So, the question is, you know, why do you think information theory is the way forward in life today? What physics is going to pick up in the following way is that bringing up the wave theory, that looked like it sort of was going to make sense of this calculated immediately later development that is the theorem which showed equivalence and Hilbert space theory, but it's against that background that it seems to me it... These are natural constructs which we get from some of them in the same spirit that Einstein approached In this situation, why the information theory rather than anything else? Well, because what seems to be puzzling when you go to an academic theory is basically what you mean by measuring information. I mean, rather it seems appropriate to come up with a principle to try and see whether you can show the points. That was sort of the basic idea. Then you ask, well, why relationalism? Well, that seems to fit with the whole idea of information as fundamental in the way that many ways you think of interpretation of quantum mechanics. What we should try to do is derive quantum mechanics from some simple assumptions, just as the first step in Einstein's By the way, this thing, this issue of measuring especially black boxes, I didn't mean, does anybody want to comment or judge yourself? What role do you mean by information in your characterization of the act? So what role do you mean? Can I just take a very agnostic view and say, look, I just have a... You mean why the constraints should be taken as referring to information at all?

45:00 They... Although formulated in terms, I don't know, I'm not sure how to say the question correctly. I'm not sure I can read the substrates in such a way that they don't do the information. You're parsing the question. I mean, I have good hold on why he wants to, thinks information is the way forward, right? I mean, he accepts this argument that that's the best way to go, to cash out. What's objective and subjective, so on and so forth. I wonder, and I think this is clearly similar to what Michael just said, do you have a similar kind of motivation that leads you to information theory? Well, the motivation is that... Interpretation is the difficulty, the human facial difficulty, of using the mechanics, which I can refer to the basics, but the basic problem is moving to an alternative theory about information and equalization of theory in terms of science constraints. All represent the nature of the physical world in which those sunscreens fall. This is sort of a question for, well, for the three. I worry that in focusing on the non-commutativity of properties, you strip out too much of physics, so that it's going to be very hard to really understand how quantum mechanics explains life. That's one of the primary achievements of early quantum theory. And it's hard to see how that comes out. Purely, I mean, the information here in the framework may play a role, but it's going to have to be more. The axioms of quantum mechanics. And look at that and immediately see that the hydrogen atom will be stable. Look at the axioms of quantum mechanics and see that H-bar has a certain value. None of this stuff is in the formal framework to begin with. And all this talk at least... So the two of us, I think, is just about recovering the formal framework. Now, if you want to do physics, what I mean by physics now is, you know, you put in your puncher in the labs in the morning and you go in and you say, guys, this is what we need to do, a laser on the table, then you have to study loads and loads of the variables that are sitting in that formal structure.

47:30 Now where does that come from? That comes from the experimental practice and this and that and so forth. But the formal structure is already there waiting. I think it's a little deeper than that. I think if you want an issue that everybody in the room is interested in, it's this solution to the measurement problem, right? The measurement problem is partly a problem of how the classical world works, or is it a quantum problem, or is it a dynamical problem about actual physics? I mean, if you don't think that that's a problem at all, then maybe, from Jeff's perspective, from a strictly instrumentalist, Jeff's earlier perspective, from a strictly instrumentalist perspective, measure the problem. Yeah, I do think it is, because I think it's not a problem. I think it's been a mistake for a lot of years to get confused about what quantum theory should explain and what it shouldn't. See, for instance, from my perspective, I would just go back to classical probability theory and say, There's an agent, and that is a piece of data, or a piece of data is given to him, and he conditionalizes fire, a piece of data, conditionalization. Is there a measurement problem there? Is there anything that's mysterious about that? I think most philosophers would say, well I don't know about philosophers, I shouldn't speak for them, but there is no measurement problem in the idea of conditionalization. When we go to quantum mechanics, I say, let's look at this formal structure called quantum mechanics. Is it more a direct statement about the world, or is it more like probability theory? And, you know, the light bulb is, oh, it's more like probability theory. And where there's no problem with classical probability theory, there is no problem in quantum mechanics either, so there is no measurement problem. I need to find some explanation. I need to find some deeper mechanism to transport the piece of data I have gathered to update from a prior to posterior. And what I mean by prior in the quantum setting is an initial quantum state, and what I mean by posterior is a final state. I keep pressing everyone on the question of why information is so important, why this is the essential thing. And maybe, Chris, I can start by asking you. I'm listening, I'm trying to hear, you know, what's absolutely essential about information?

50:00 And what I hear in your story is that the quantum mechanical... Mathematical structures that we deal with are incomplete descriptions of some sort, and so they're involved with information. But that doesn't seem to be restricting. The possibilities vary greatly. There are many theories that use incomplete descriptions. Why is the notion of information itself, which carries so many connotations for us, why is that so essential now to understanding quantum mechanics? It's the thing that we've missed for 70 years. I'm just not seeing where that comes from. I don't think we've, you know, there's been a small number of people that haven't missed it. The same people who didn't miss it didn't have any form of clues. One thing that's new here, at least from my perspective, is that we have some informal physicists have a little more familiarity with Shannon and so forth. I differ from Jeff in taking information as anything fundamental to the construction of the universe. Jeff says that we find that physical theories are about information. So Jeff says that information is no more fundamental to the universe than the concept of love. Will the universe be roughly the same except for the absence of those entities? If you delete from the universe those entities which are capable of processing information, what information is crucial to me, indeed, is this issue that it's the evidence for the view that quantum states represent incomplete. Maybe I'd say incomplete information, but that has kind of back-developed what Chris was talking about. I'm not giving talks, I usually say, yeah, you know, we could be talking about classical mechanics, we could be talking about classical linear billion mechanics, and be talking about incomplete information. There is a difference between classical linear billion mechanics and quantum mechanics, I believe. And one difference is, classical linear billion mechanics is incomplete information about pre-existing problems. I don't think that that interpretation holds. What it has in common with classical liability mechanics is it's again about incomplete information, but incomplete information about something that will come to be in the measurement process. So, both of those things are about information.

52:30 What changes is the characteristic of the argument. When I have P of H, P of some hypothesis, in the classical case, I can think of the hypothesis as pre-existing the act. And in the quantum case, I don't think it's productive to take that point of view. Ultimately, you can because of the existence of linear mechanics. So I don't think it's productive to take that point of view. So why isn't that it? Why isn't that the key point for what distinguishes quantum mechanics from... Well, it ultimately will be, I think. That will be the key. But one thing that we have to do first is separate all of the objective pieces from each other. So you might think, well, along with that one key point, maybe there's another one. And this other one is that quantum states can't exist. Or maybe it's not only the non-pre-existence, but let's say it's in the past. All I see this effort is doing is clearing away all of these other things that aren't the key features. Utilizing or identifying all of the things that are about incomplete information. So you can say, I don't care about that. I don't care about that. I'll throw it down to this place. So I see this as a tool. I would say that the kind of non-commutativity, the kind of non-commutative mechanics that we seem to be characterized, and can be characterized, by supposing that there are, for me, the kind of non-commutativity, by kind of non-commutativity, I mean non-commutativity. If you tell that sort of story, you're saying that these so-called or claimed information through any laws of nature are not laws of nature because they're actually false, or they will turn out to be false and also say that, well, as a matter of fact, you know, we have a... The laws will hold, so there are only laws which hold in there, and non-commutative mechanics, which is puzzling.

55:00 And you relate the puzzlingness, well, I tried to relate the puzzlingness to a further question maybe about how you understand information. But it seems there's an interpretative problem about this non-commutative mechanics. But it actually needs to be solved in the following way. Non-communicable mechanics is actually quite likely false, and we may just be headed here, putting our hands against the wall to understand some false theory. But it might also be true, you know, and if it's true, then we might want to understand, you know, well, what helps in information theory laws. Now, I think it is legitimate to say, well, you know, what does that really mean? But if you're saying that, aren't you really just being a mentalist and so on? So I try to suggest, without really spelling it out, that a natural way to move, I'm actually not even sure, I'd try to suggest a natural way to prove which fits with the claim that their information theory laws are applicable to our world is that our world is a very understood relation. So that's the way I see it, but it seems to me the fundamental problem is to be by a puzzle that you get when you move from a commutative to a non-commutative mechanic. Now, on the issue of, well, there's this information, there is a space that gives you all of physics, it's not supposed to. What it's supposed to do is to characterize broadly The structure of the sorts of theories that you can have in a world in which information theory first goes whole, you have to then do some things about specific kinds of physical systems, and the claim is that, well, you know, you'll do that, and the broad structure of that theory will have to be, you know, a number of C-star algorithms. Of course, you don't get, I mean, we don't intend to. These move and give you some constants of nature to give you specific... Maybe stop at the last few minutes. Oh, sorry. Oh, I'm sorry. So, the other thing, I'm not quite sure how... I'm sorry, I was kind of looking at the camera. So, I'm not sure how the idea of relational fits with information.

57:30 Special relativity, relation theory, non-velocity, and so on. But a couple of quick points about what Chris said. The measurement problem is not a problem. So first of all, the idea that there's a way to measure...