Zeilinger's Foundational Principle for Quantum Theory (contd.)

0:00 There, the idea of what's supposed to be the elementary system. The elementary system, if we look carefully, is defined as a system which is represented by the truth value of one proposition. So, in the bone theory, what's an elementary system going to be? It doesn't look as if there is going to be any such thing as an elementary system because it actually wants to make a very strange promise of the system because we have a configuration or a continuum of possible things. So, in this case, the foundation pencil is going to be doing no good because there's no such thing as an elementary system. This is a slightly pedantic point of Bohmian that has been talked about, there must be infernal structure in corcassals. Yeah, there's a bit of a muscle when we talk about it. Is there anything you think? Infernal structure in corcassals. Yeah, I don't think any serious Bohmian would say that. Sorry, why would that help? I was just saying that... There might be elementary proposition, elementary systems within that. But I think the more serious point is, is this guy really talking about trying to find, is he talking about elementary systems as the smallest thing we can find? Because you could, what you're saying about conceptual resources, You could say that the person was an elementary system if your question was, is that a person? So, it does very much seem to be . Well, I would agree, but he's talking about microphysics. So, he's trying to find the very, very smallest. Well, I think there is a tension here, because he's sort of trying to use the language of quantum information theory, how much can we encode in the system. And there we seem to have some handle on information. We have seen to have some handle on system. Physical, the system is a physical thing. And then what can we do with a physical thing? But his language is, the way he's thinking is thoroughly Copenhagen. It's all about how can we describe the world, the way in which we describe the world is everything. And so there's, I mean, these two don't fit together well. And I think it's why this, one of the reasons this foundation principle ends up being completely vacuous.

2:30 Just to finish up, it tries to explain entanglement 2, although I must admit I haven't read properly in my recent paper. Generalizing the foundation principle, elementary systems contain n bits, so entanglement results when these n bits are also specifying joint properties of the systems alone. Remember what it is to exhaust bits of information, it means that the length, our vector, is all along one projector, which meant representation. So it's just saying the state is an entangled state. So, that doesn't work. Finally, in the conclusion to the paper, Trice says, I think my foundational principle answers one reader's big questions, why the quantum? The most fundamental viewpoint here is that the quantum is a consequence of what can be said about the world. Since what can be said has to be expressed in proposition, and since the most elementary statement is a single proposition, quantization follows if the most elementary system represents just a single of a proposition, a bit of a howler. Quantization only follows the propositions of one-dimensional projects in a complex, separable hill to space. Why is it that the world has to be described that way? That's the question that he is answering. That's what that question's saying. There's a definite tractatus flavor to the black quotation. I think there's something about Vienna that does it to you. I thought it was only propositional logic when you got from the picture theory of learning, but you couldn't even get quantization out of it. You look hard enough. I might use that number, do you like that? Sorry for going on, sir. Thank you. Any more questions? I don't have another question I'm just going to ask so many, but I do think you've got enough material to talk. Very impressive afternoon. The trouble is it's not sufficiently interesting if we had another half on it.

5:00 So you could separate the information that the way you criticised their new ITOT, Mrs. Shannon, from the fundamental principle tool. Yeah, but um, I didn't get my foundational principle stuff last week or in the last couple of days, so I'm a bit more shaky on it all the rest of it, which is perhaps what is more natural extras. Ha ha ha. I'm trying to be extra. But I'm glad, Claire, that you saw what was all longer straight away with that bad position, because I think it's, um, I thought there was something hideous in the world as soon as I saw it. I think it seems to take it very seriously and get a lot out of it and maybe say anything about it. So, yeah. But are they explicit about this connection with, uh, Farno and Iranovich and so on? Do they see that geometric aspect of their proposal? I'm not sure that they see it. I've found those papers from some of them from following their references. But I'm not sure that they actually have that geometric understanding of why aren't I laid out there. Because if they do, I don't see how they can make the claims that they do. They've proved that equation, the relationship between the individual measure and the total information. Well, I haven't actually seen Brittany prove it in his PhD thesis. And as in trying to prove that myself that I came across this way of representing it and thinking about it. But I'm not sure for what extent they grasp this too much. I agree with you, it does seem to be, as far as the Achilles, it's not a disenfranchisement which says that the world must be digitised in the image. Well, why doesn't the proposition, why does the yes-murried thing have to be discussed?

7:30 Well, if you start with some very kind of down assumption, you're also going to describe the proposition and you're going to have to come down. I mean, if you haven't got a continuum, if you're starting to make a proposition that one, you haven't got a continuum in the American effect, I think it's important. It doesn't seem to be interesting, but that would be any of that last question. It doesn't answer any of the questions you've actually had in the end. Um, so your thought is perhaps that if we take the more information we're being put in here... I'm sorry, basically, not the end of it. I think that, because it says that forces, you know, described as some of the religious opposition, which is very important. that you can chop us down to small pieces and then you will just try to squeeze just a second and then you get down to a small chunk There's no reason why a single proposition of its own describes anything I'm not trying to defend something, I'm trying to I'm slightly more reasonably except for the family But if you were going to do that on your own, would it help us that you couldn't take the continuing movement in the house? Are there any members that are in the cabinet, any motivations? Yeah, just the analogy that my mum before me said that they're members. and it's where you're accepting these things as where you maybe can't have their time for description. So you're getting instructions out and you don't have much of a mistake, isn't it? Yes, but if you'd be really willing to have to throw out the things that you've ever done,

10:00 I'm sure it depends on the language, is it, just because you've got countably many propositions, Propositions doesn't mean that those propositions, I mean, some propositions, maybe they can only have a model which involves non-counterable, non-counterable balance. I think there's a little proposition to be about, certainly. I agree with you, this is our question. Shouldn't there be more investigation into the collection? between the first two principles that said everything's describing propositions, one bit is elementary. So there'd be more sort of an investigation whether those two are identical or whether they want to follow the other by how you're going to set up your notion of information, what your alternatives are going to be in. I must admit that I had probably zoom in through the mathematical bit at this rate. episode probably you may have an escape about there or later I think you're right there what precisely is the relationship between these basically you said that the the elementary system carries one bit of information because given the one you could either say yes or to the proposition so that's what the relationship whatever the proposition the proposition bivalent opposition, then Bet is supposed to just say that it's true or false. How's that going to bear on his choice of information, information calculus math, Bet later? I don't think directly related in an interesting way.

12:30 There's a question about whether we should take a bit as an amount of information, given it measures information in a way which doesn't show any way. Yeah, it's just enough. But I'm not sure how telling that is. I mean, he's, being a sort of a Copenhagenist kind of guy, it's classical information is what I'm talking about. Um, so, and for classical information he's happy with Shannon, where I'm thinking about things. So, I don't know. It's possible that there isn't enough to talk about anything. I want to just ask a general question, whether the von Neumann Entropy and the IP or IRO of them, are they for each of the members of wider families, like the Shannon is a member of this Renny Ufi family? Well, there's a relationship. One of the bits I skipped is explaining how the functions of the state are related to the e.g., the border of entropy and the token information are related to the Shaman information and the book and the diary of it. and so I'll just stick that up. What's one of the relationship between probability distribution, which is an interesting relationship, which can be made by relation relation, which is a pre-order, Q is majorised by P, if only if Q is a mixture of permutations of P. So, since it's a mixture of permutations, Q is more mixed. Now, it's like a coarse thing. You just re-label and then you aggregate. Then I showed you Yost's general part of uncertainty measures, very simple, they're just the inverse of measures of concentration. I said that there's an important property that they're share convex or share from K. Just an explanation of why these are

15:00 interesting properties. If Q is more disorder than K, Then if we have a sure convex function of Q, it's less than that function of P. So that's a measure of how concentrated it is when you pull more gray vectors down. And sure, concave, it's a very round measure of uncertainty because the more coarser one that the mucked up disorder one is more uncertain than the anatomy one. Then these relations, majorisation relations, apply to vector driving values for density If rho is the pre-medium state and rho dash is the pre-medium state, then lambda dash, that providing value of the pre-medium state of the main line, that lambda, that providing values of the pre-medium state, to provide the form of the distribution of the main points of the vector measures with more disorders that spread from the other values of rho. But that's the fundamental relation. And then we can just do different functions, It's effectively tell us that then and over again. If you, for sure, concade function measures uncertainty for example, which I'm interested. Then, it's a concave one, so more of a sort of one. Conction more of a sort of one is greater than the one. H of the vector-origin values is, of course, the one I meant to think. So that is the so-called Heleno bound? No, no. Heleno bound is talking about neutral. Oh, sorry. Right. Anyway, you're getting extra. Von Neumann is upper bound of scan there. Yeah. Right. And that tells us why the measure of mixness of Von Neumann HP is a sort of measure of information, how much we know, because the greater the maximum, the more uncertain it must be about the outcome of any given measurement. Any measurement is more uncertain than the eigenvalues of the vector eigenvalues of the eigenvalues. And then it's precisely the same, they have a relationship between the written dining and measure and the paper information, given

17:30 the same thing, it goes the other way because this is a convex function, the structure is the same. The total information content is a measure of how much you know given the state because of this relation. um, could break the isotopes, the um, the more amazing we are, you know, so it's relatively bad in my thought, but that's where we are. So, the greater good, the better good outcome. So, for any, um, of the class of, uh, of uncertainty or concentration between the function of the lateral line values and the probability distribution of measurement. Could I make a supplementary that I vaguely remember, Harvey will remember, when you asked the theory a few months ago, he gave You just talk about the statistical and mechanical realisation of the lead-in-buston axis. And it's all about that relationship, as I recall, between your pre-order, was right in there with his construction of realisation of some of his lead actions. It's a period of majorisation in a very neat way of bringing together a large amount of discussion of these sort of issues in relation to mixing, mixing, enhancing, and all that sort of stuff. If you're looking, for instance, in Alfred Wiles' review paper on entropy, he has been pulling many, many different ways of proving what is essentially a fact about major evaluation of matrixes, and Nielsen has actually used major evaluation stuff in some ways recently, particularly as a condition on a entanglement transformation. So it's a very powerful relationship because you told us about the interesting in relation to the community distribution.

20:00 It's quite well, it's 4 o'clock. It's a little bit of a patient level, I'll have to cut that part down from that. it was several excellent talks certainly at least two Thank you. Thank you. Thank you. Thank you.

22:30 I mean, I have to update you, because it's changing whatever it was, but that's not a problem. I mean, it's a very, very... I mean, I'd like to say that there are two and three ways to do, I mean, there's three that say that they won't have other things and that's just you know the answer is the reason you sort of crack your brain you know is that the other one which is what I would intend to do well I wouldn't I don't know Thank you.