Quantum Information Theory — Part 2

0:00 We capture the distinction between the two notions of information and allocutions of this kind. Because what this suggests is that in information theory we're talking about a part of the everyday concept of information. We're ignoring the fun stuff about what the information might be about or what it might be useful for. We're ignoring that, but at least we're talking about the quantity of that stuff we might have around. But that's simply not the case. We're introducing a new concept which is completely orthogonal to the everyday notion of information. And we certainly can talk about the quantity of that thing. But we're not talking about the quantity of the everyday notion. And we don't get that sufficiently clearly from these kinds of phrasings. And the second point, our really important point for today, is that it's just wrong that we're only dealing with the quantity of the information that we've introduced, this technical information that we've introduced. We certainly do deal with the quantity of information that we have already. But we also, if we understand the coding theorems properly, We also have a perfectly good specification of what information in the technical sense is. Coding theorems both tell us what information is and how much of it there is. But it's that point that what information is can be, is indeed already specified. It's just there, it's there in the face if you think about the theorems, the definitions and so on, define the theory. is that fact that that specification is there in the theory that allows us to say what information is and then what quantum information is ok so takeaway point we can say more than is commonly supposed about the definition of quantum information because we have a quantum coding theorem that introduced the notion and that specifies what pieces of information are as well as how much information there may be around and this is something that might come as a surprise and good people have thought it can't happen and you don't have this thing. So, for example, Horolevsky is saying, well, quantum information, sure, it's a fundamental concept in quantum information. It's not a precisely defined one. No, I submit it's perfectly adequately and clearly defined if you pay attention to the right bits of the statement. And here, Richard Yosa, a strong review, says, quantum state psi may be viewed as a carrier of quantum information which we need undefined in all fundamental terms. new concept, no classical angle. Primary fundamental concepts are inso facto and defined as a definition

2:30 amounts to characterisation in yet fundamental terms, and they require meaning only afterwards from the structure of the theory that they support. So here we have that Hilbert-side idea of implicit definition giving us meaning. But I submit we can, or we have, done better than this. We can have a definition, but if we do have a definition of quantum information, And it turns out it's not the case that there's no classical analogue, there is a classical analogue, it is just classical information. So I'm going to tell you a story now about how we can find, within the standard structure of information theory, the generic definition of what information is, that we suppose classical and quantum information are species. And the thought, actually, is extremely simple. we just go back to Shannon and his other papers from 1948 and his original characterization of what one's up to when one's trying to write communication through what one's up to when one's trying to conceive an information theory the fundamental problem is which he is concerned he states the problem then he can go on to try and solve it the fundamental problem of communication is that of reproducing at one point either exactly or approximately the message selected So reflecting on that for a moment, we can come up with a simple definition of what information in an information theory is going to be. It's just this, I suggest. Information in the technical sense of an information theory, I'm going to try and substitute this with the TV theorem, so there's no chance of confusion with the everyday notion. Information in the technical sense is what is produced by an information source that is required to be reproducible at the destination be counted a success this defines what information is and it answers already certain important questions about the nature of information you'll notice of course this is actually a very general very general definition but actually i think that's a good thing it's the kind of generality we ought to have in a definition of information which is fitted to shannon's original specification what one thinks one's trying to problems one's trying to solve their communication. So there are several aspects of generality. The first one is what exactly is it you're trying to reproduce over here, you want to reproduce over here. So different stories about that are going to correspond to different stories about the nature of the messages you're sending and thus the information you're sending. Classical reporting will provide

5:00 wonderful examples about different, you're interested in sending different kinds of things and you're producing different things. And the related ideas, what counts as successful and what you're trying to do. The final component of the definition, which is unspecified in the definition, is what an information source is. And here I don't have a particularly useful general statement, but the way one introduces the notion of an information source is by just looking at a Shannon paradigm. An information source is the kind of thing that Shannon introduced, and Jeff already nicely explained that a Shannon prototype of an information source is this morning. The channel information source is just some physical object which we can see which we can characterise as a black box which spits out various systems in certain particular classical distinguishable states with a certain probability. If that's an information source, the message produced by that is going to be some long sequence of systems, each one in one of the particular possible states that can be produced and having occurred in a sequence with a certain probability and the sequences are large length n and then we can talk about compressing them because of the redundancy given by the probability distribution. And so you point to the specified information source, you point to the Shannon Crowe stuff and then you think about generalising it in various ways and that's what Ben Schumacher did in the early 90s to get the concept of quantum information. So a quantum information source is again just something you can characterise as a black box which spits out systems prepared in particular quantum states could be mixed pretty pure, just for simplicity and time, we're going to have to take this on the pure case today, with some probability that's a quantum information source now the message in this case is again, going to be a long sequence of systems each one of which is in one of the yeah, each one of which is in one of these quantum states get some water So we have our notion of information source And we actually already have our notion Of what it is that they produce Time to set it Tell me what that's fine They produce sequences of certain states In the classical case it's a sequence of Distinguishable systems in distinguishable classical states In the quantum case Sequences of systems in Non-distinguishable typically Quantum states

7:30 So what we have been produced are tokens of a particular type. The type is the particular pattern of states that are instantiated. The token is the object, the physical object, instantiating those states. And so now to get our philosophical payoff from all this, we just need to ask, well, what's the information? Information is what's produced by the source that requires it to reproduce, or reproduce over it. What's the information then? Is it the type or is it the token? If it's the token, then information is a concrete thing. If it's the type, information is an abstract thing, it's not part of the world. And the answer is, it's the type. Now, the quick way to see this is, so if Alice once has a certain message produced by her information source, she wants to send it to Bob, one way she could do that is just by sending him the concrete thing she possesses, the token at the time. That's one way she could do it. But she need not do it that way. In a classical world, she can make a copy of it and send that to Bob instead. Then they both end up with two different tokens of the same type. and that would count as a transmission of classical information too in this case so it can't be the case that it's the tokens that are what is produced that's required to be produced because if that was so she'd have to send what she's got to him but she doesn't and the same holds in the quantum case so it's the type and the quick way of seeing why it's the type we refer to when we're talking about pieces of information produced by the system is that when we specify what's transmitted we do so by sequence types and not the concrete things themselves. We can say, oh, it was a sequence A1, A2, A3, A4, 0, 1, 1, 1, 1, 1, 1. We specify, we describe a sentence type and say, oh, that is not a sentence type, but a sequence type. And it's that that needs to be reproduced at Bob's side, reproduced or reproduced, so if he reproduces, he ends up with an anonymous token of that type. So, it's interesting what happens in cases where we have the systems produced by the quantum source are actually entangled to other systems, but we haven't got time to go into that there. The analysis I've just sketched works for those too. So pieces of information of what the output of the source is, whether it's quantum classical. Pieces of

10:00 information are a extractor, they're tight, they're not part of those basically temporal contents of the world. Bits of information, it's interesting to note, of course, we do have the quantitative as well as the qualitative aspects of the notion of theories of information. Quantities of information noted by the Shannon information, which will be metric in the quantity case. Tell us about compressibility of the source. How much can you, what's the minimal amount of resources that you can squeeze what you produce onto in such a way that it's reproducible at the front side. But notice that if we're interested in quantity of information, then because that's a type, sorry, property, compressibility is a property, properties are abstracted too. on the bits or the pieces, information, term information as an abstract noun. Summary. There exists a general definition of information in the technical sense, in which both classical and quantum information is assumed. You get the difference between the two cases by specifying the differences in information sources and the differences in what counts as success. It follows that information in the technical sense is abstract and not of the contents of the world. So it follows the pieces of information that are lacking in spatiotemporal location. out if you're ever tempted to get puzzled about teleportation. Long story there, it's fun, but I haven't got time right now. So, in short, something to you is wrong. Why does this matter? Let's go back to three tantalizers. So, information and materialism, information is physical, information and quantum measurements. Does quantum information theory support information in materialism? Well no, not on this analysis. Because even if you have a theory which spends all its time talking about pieces of information and how they manifest in the world and how they change and evolve, we're not going to get rid of the tokens which are needed to instantiate the types that we're there by talking about. So that means that you need the physical stuff along with the higher level properties of the physical stuff you're interested If you're to have a story about what's going on in the world, you can't have the one without the other. Now, that doesn't mean that one can't be an immaterialist, because you could just have an immaterialist analysis of physical systems to start off with. And then you say, well, look, the token's immaterial too. But our question, I mean, I think that could be totally and wildly plausible.

12:30 But the point is that quantum information theory certainly doesn't support any form of immaterialism, because it makes no judgment about the nature of the token. So informational and materialism There's no support from it From the point of view of talking information through Not one jot Information is physical Well, there are various friends one can Put apart here The short answer is that it's false to say That information is physical Because this is a category mistake So pieces of information per abstractor They're not concrete things The types aren't physical The tokens are physical That's not what information is so information is physical as a category and information in quantum measurement I've got lots and lots and lots to say about this but now there's no time so I'm letting you off the hook there so finally, the hand wave is still I hope I've explained to you why I think the right view of quantum information here is a view not in which quantum information is a new kind of part of the contents of the world which behaves in certain ways but rather information in this theory, the term information is an abstract noun, pieces of information aren't concrete things. So the quantum information theory must be a theory about certain higher level properties of stuff that's already there and which the fundamental theory tells us about. So that addresses the question of whether information in something in a technical sense, channel-esque sense, might be a fundamental physical concept in at least one way. But it's probably more than one could mean, more than one thing that one might mean by X as a fundamental physical concept. There are more ways than one perhaps have been fundamental. But anyway, my conjecture is no, information in the technical sense is not apt to be a fundamental physical concept. Rather, it's an adventitious concept. It's of the nature of an addition from without. It's an addition from the perspective, the parochial perspective of people who are interested in sending things to one another. You have the world doing its thing. You can have a complete description of that world, the theory, specifies everything else that used to be said about it. And then you might have some people who actually exist in the world, and they're interested in using certain properties of the world to do various things. But those people, it might be infusible to introduce the notions of quantum information theory, compressibility, the kinds of constraints and what you can do. Certainly that's useful for them. You can tell a complete story about how the world is without having to use those notions

15:00 or so I would maintain. Information is an addition from without. And finally here's a sort of a philosophy of science, methodological kind of consideration. Quantum information theory is a rich, interesting and in some ways fundamental kind of theory. And it's certainly given us progress, substantive progress what the lesson I want to draw from adopting the definition of the argument of quantum information for active pieces of quantum information is that it's not the case this fact is obvious to people it's not the case that fundamental physics need always progress by postulating new kinds of things sometimes it does progress in that way and it's fantastic and it does but it needs always progress in that way and this kind of phenomenon is something that Jeremy Butterfield has drawn attention to in his work on analytical mechanics so analytical mechanics is of course an extremely rich and fruitful framework, but at least when it was introduced it didn't introduce new kinds of things into the world, it allowed us to ask and answer various extremely complicated kinds of questions we couldn't ask and answer before, and I think that's the kind of way to think about quantum information it allows us to ask things, interest some things, reveal but tell us about features, structural features of our theory and of the world of theory as truth and it doesn't do that the question of raising and answering a question but I don't think I'm just going to do that. There's a different way of making progress than just by postulating new kinds of stuff. And another example would be contrapeel theoretic techniques in conventional astrophysics. So I think this is just an interesting example of those kinds of way of making progress. And here's a bunch of references. Thanks. Thanks for this illuminating, that's a really controversial talk. It's all true. Mattel. Would you call velocity an advantageous concept? Would I call velocity, for instance? Velocity, what you're thinking, because it could be frame relative. Yes, that's it. Not necessarily. so no I wouldn't necessarily I mean no no I wouldn't call it an adventitious concept even though it's if it's one of the media physicists who want to talk about philosophy they could do it in the world there are objects that never left me that could be true

17:30 but if the task is to look at what kinds of concepts could be you would expect to play certain kinds of roles in various physical theories when you can answer that question which you take to be well-formed and interesting and looking at the kinds of role the concepts within them play. Now, that can progress without us having to, in any of those theories, have got it right. So to some extent, there's a disconnect between which of the theories is actually true and how the concepts in the various theories function. I mean, it's as if there were good kinds of concepts which were apt for truth should the world be such and such a way. Michael. fundamental concepts. In your denial that information is fundamental, does that mean you are ruling out JetBlue-type programs to axiomitize quantum theory using information as a fundamental notion? No, but I would be saying that one wouldn't be revealing the fundamental nature of quantum theory by doing so. But that's just a claim, isn't it? Okay, well, so it depends, because one can do interesting work. I mean, so this is part that comes on long story for another day one can make progress in understanding the nature of quantum mechanics by locating quantum theory within a theory space I think that's a fascinating and interesting thing to do but I don't think it necessarily engages in fact I think it typically doesn't engage with the question of what the ontology of the theory is I didn't say anything about ontology I'm just talking about fundamental concepts if the claim is the characteristic thing about quantum theory that differs from classical should be spelled out in information suggests to me that it's a fundamental concept, the quantum theory. That's right. And so you're denying that it's, because you were kind of, that's what I was wondering, you were kind of conflating fundamental concept with postulation of a new kind of thing. No, I certainly didn't mean to. I mean, that's part of the point of saying there's more work than one way. So I don't mean to be talking about postulating anything. I just mean to be saying if this is the fundamental way to see the difference between quantum and possible things, doesn't it follow that it's a fundamental concept? In one sense of fundamental perhaps so, but notice there's an important caveat, right? So information theoretic axiomatisations may not be the unique things that pick out the structure of quantum mechanics in theory space. We've made pretty good, I mean these guys have made good progress in saying that we can get quite close to quantum mechanics.

20:00 so even if we found that there was an information theoretic characterization which picked out what we think were particularly germane features of quantum mechanics compared to other kinds of theories that wouldn't yet establish that those principles were fundamental because there could be other kinds of actions that would do it and we could also question that, I mean it's interesting that you use the term sort of characteristic features that's a level of abstraction away from the content of the theory to some extent, so talking about no cloning rather than talking about what states have and what kind of dynamics they can be subject to, is a level of abstraction which may be significant in pointing to pertinent differences between classical and quantum. One might well not capture the entire content of the fundamental theory, sort of physically fundamental theory in the case of specifying what there is in the world and how it behaves, by postulating those features. Howard? So I guess my question is going to relate a little bit to my question. So it seems to me that there might be a sense of information in which it's not necessarily a little different from what you were talking about. It's not necessarily a sort of independent trial. and so in relation to Michael's company said if the proper way to formalize if it turns out to be seemingly fundamental formalize the and maybe that is something about quantum mechanics I don't see how that could follow because you could always imply a realist interpretation of what you end up with if you recover the structure of quantum mechanics and just wheel out your favourite realist interpretation of it, you no longer have an operational standard you can't do two things at the same time you can't recover the structure of quantum mechanics and rule out any possible realist interpretation because realist interpretations which are intelligible Well, so if they're not, if the realist interpretation, so I guess the claim of the realist interpretation has to be Lorentzian and the fundamental, not illuminating to couch these results that some of the correct ones want in those terms.

22:30 That was Jeff, sorry? The Baldwin theory, for example, Jeff says, is Lorentzian, and so it's not the fundamental. Yeah, so I mean, I totally disagree with that use of the rinsing as a pejorative phrase. I mean, it's the wrong analogy to draw. So, sort of along those lines, I was wondering, so Chris folks in Richard Joseph, and I think probably he was a bit of a while back. It's a work on quantum coding of mistakes. And I actually got into it, especially Richard, this one confirms your take on it. I think I would take your view of the way to do it as being the right one, but I wouldn't necessarily want to tie up to a subjective probability. I want to try and remain neutral on whether it's a probability of an objective or a subjective. Thank you. Paul is next. Something that I feel we left out I think it's, when we put it in, it's going to be consistent with everything you said, but has some important consequences. Start off with, again, the notion of quantity One way of understanding that, quantity is the number of discriminations that one can make. Not the number of binary discriminations that one can make. And you're forgetting about the probability of distribution. But it starts with the number. Well, not necessarily. That's how Hartley did it, but that turned out to be the wrong way of doing it. Let me start with that, see if we get whether the difference you have in mind makes a difference and if it does, I'm going to get a lot out of your time. So one way of trying to think about quantity of information is in terms of numbers of discriminations that would be made. But when it comes to content of information, the question is how are those discriminations interpreted? So, right away, we have the suggestion that if we have a notion that goes beyond measure

25:00 and its content, the notion of interpretation is essential. Proof by example, Alice sends the same sequence of zeros and ones to Bob and Carl, but Bob is, the question is, if one reads it as binary and the other as decimal, different messages. Even the notion of the same token involved interpretation is the V in small letters the same as the capital letters as a matter of interpretation. Now, consequences. Does this mean we can't theorize about that? No, not at all. Because what goes on in these theoretical studies is certain things about the interpretation are held constant. For example, how a sequence of zero in lenses can be interpreted. Second consequence, a very strong reason for thinking that the notion of information as content can't be a fundamental physical concept. Third consequence, does it in any way show that there's a problem with at least using facts about information to illuminate it, not to completely capture what's in quantum mechanics? No, it doesn't have that consequence, because those limitations can be put, again, in how many discriminations can be communicated. And I think if we go back and think about Jeff's talk, I at least think I can reinterpret the line of argument in those terms. Good. So I agree completely with some of what you've said, but other parts of it, I think, a subject needs to be made with distinctions, which I didn't have time to do today. So on the point that we need to kind of fix up in advance criteria of identity for type so we know what one token is, what counts as being a token for type. Yes, I mean, that's absolutely true. And that's going to be, I mean, this is one of the reasons why the notion of information in this technical sense is going to be an adventitious one. Because Alice and Bob need to decide, they need to both share criteria for type identity find the path. That's not something the theory should deal with because it's going to be too genuine. But the stuff about interpretation, so this slide up, the sort of interpretation when we have related to genuine semantic content is the move from meaningless types, so sentences

27:30 can be considered just as a particular structural thing rather than things being endowed with out of the meaning and they're apt to express propositions, but if you just consider them as purely structural features of them, then they're just, they're possibly not even syntactic, they're just particular structures of things. Now, the level at which Shannon's theoretic or quantum information theory work, it's purely at that level, there's no semantic kind of content, there's no question of meaning, there's no questions of interpretation. If you want agent sees some particular outcome, you know something about a probability distribution, you're able to infer something about something else and let them to gain information thereby. That information that you've gained isn't something, isn't the information that Shannon information theory talks about. an everyday notion of information. Let's talk about that. Okay. I think Lucy had a question. So there's something very strikingly about what was described So, for example, if you take a screen heart, or you take polarization to be a freedom of an electron, or if you take the path taken to be a freedom of an accident in a chronometer, or the other examples that you think of, each of those examples is described by two-dimensional photospace, and there's a mapping between the physics, the sort of measurements and preparations, or translations between each of those cases, you can map them. And then the same is true more generally for physical situations where you have a given number of devices, reliably to see what's going on in the space. Basically, that translates into the dimension of the global space. So there's something physically the same about multiple situations, which is surprising since physically they seem like very difficult situations. So, whatever that thing is, it's difficult to regard it as an addition from that. It seems like something that's very much all within the building. Nice, nice. Yeah, very suggestive consideration. But, particularly Mark Sender, Patron, and Walter Prometh, what really is that? I mean, we've got two different modes of the electromagnetic field. That's really what's going on. Have you excited for this mode, or have you excited for this mode? So, if you want to describe it properly, you should have your, as indeed our physical commitments,

30:00 if you say what's actually there and what's actually happening you should wheel out your quantum electron dynamics and do it like that now it turns out there are structural similarities there are structural similarities when you abstract from the physical details there are structural similarities which allow you to do this just take a couple of degrees of freedom they're distinguishable just represent it in a Hilbert space and I think you're dead right that quantum information theory highlights these interesting structural similarities but they're not and it's because of interesting features of the fundamental theory, the field theory that you can do that I don't think it is because we wouldn't even notice them if it weren't already true that the fundamental theory allowed us to make these approximations It's a bit classic as well they can use blackboard, pink, brown, blackboard, zero, and all it's not a surprising classic because a simplet is not such a surprising what does it mean is one more surprising Doesn't this suggest that the underlying analogy is more of a hardware-software analogy than the type-token distinction? Hardware-software. You mean the realizability? Conceivably, but realizability is all really about types of tokens and tokens. I'm not sure. Last question from Rob. So, concerning the different meanings of the word information, it seems to me that actually I can distinguish three meanings. That's probably all which I already meant. Yeah, well, I think these are sort of three meanings because they need confusion. So, in the beginning, you said many textbooks start out in information theory, kind of distinguish thinking that information is the meaning of the bit string or the sentence as opposed to the bit string or the sentence itself. so you could say, well, this communication channel transmits information, even though the person on the other end might not have a meaning of this but there's a second confusion which is that often in communication theory we talk about information as a measure of lack of uncertainty Yeah, so Howard kind of mentioned this, but you're dead right that's Shannon's fault, he confused everybody at the beginning it was a bad thing, uncertainty and Shannon's information are again, orthogonal concepts, they're logically distinct this is just a comment and the one thing that for me really really drove on that latter distinction was who thinks example of how so you know the example where you can acquire new data

32:30 about the world. And you get more uncertain. Yeah, you've increased your information and yet your uncertainty can go up which means that sometimes you're getting a decrease. Yeah, that's right. So if I want to know where my keys are there's a high probability they're in my pocket. If they're not in my pocket they could be anywhere, I look in my pocket they're not there, bloody hell probability distribution is bang and so I'm much more uncertain when I gain some information I mean you can get around that particular trouble but things work in general establishes that uncertainty and information are logically distinct Thank you Thanks again So the weather forecast is not very good there might be storms And it will be about 17 degrees this afternoon. Okay, yes. I have a problem to go to. It's a problem to go to. Yes, you have to be careful. You want to go to the table? Yes, no, it's too late. There are a lot of people who are going to go to the table. You have to go to the table. You have to go to the table until tomorrow? I have the impression that you have to go to the table. I have the impression that you have to go to the table. beginnings but all these aspects are of systematic interest today. Next I will talk about the pragmatic attitude. One of the pragmatic approaches and the pragmatic attitude of the physicists in the lab is to prepare waves and to detect particles. That's very important to be aware of that. Then I will talk a little bit only about the reason which way experiments because the next talk will be about that and finally I try to suggest some possible ontological conclusions under the title on what there is. So, what means wave-participality? Einstein in 1905 had his famous light quarter hypothesis suggested the hypothesis of meta waves and this is the, so to say, operational basis of wave-particle duality, or phenomenological. In 1926, Max Born suggested his

35:00 probabilistic view of the wave function, where at the left hand side is the wave function, squared amplitude at the right hand side is the probability of detecting particles at a certain position. In 1927, Bohr suggested his concept of complementarity, according to which the physical quantities of momentum and energy on the one hand and the spatial temporal description on the other hand are in clinch, but also complement each other according to Bohr's complementarity account of quantum mechanics. Heisenberg, in his 1930 in the third book on quantum mechanics explained a little bit more about this complementarity philosophy this is quite close to Boer what he makes there and I think that it's also important to take into account Einstein's also interpretation the interpretation he suggested in the Schilp volume in the reply to all the articles because he was not content with the meaning of wave function at that time and he had some kind of instrumentalistic approach to quantum mechanics finally. I will say a bit more about it later. Let me start with the light quantum and matter waves of Einstein and Vogelin. They are phenomenological relations between particle magnitudes and energy which comes in a discrete quantum a momentum on the left hand side of both equations and on the right hand side there are wave magnitudes namely frequency and the wave vector k which is proportional which is c over lambda. The experimental tests on these relations and on the relation yes on the relation between particle properties or magnitudes here and wave magnitudes there are the Compton effect where Einstein's light quantum hypothesis is somehow built in into relativistic kinematics and describes processes of impact. And on the other hand, the famous Debson and Jarma experiment on electron diffraction that you send an electron beam to a crystal and then you get a very nice interference pattern.

37:30 So this is the phenomenological basis or operational basis. Then again the Schrödinger equation and the question about the meaning of the famous wave function psi. Heisenberg's version of matrix mechanics was somehow agnostic, absolutely agnostic about what's going on inside the atom, suggested these waves, these stationary waves, and Bond in his famous two 1926 papers suggested the probabilistic interpretation in a model where he generalized was a count of stationary waves from inside the atom to an asymptotic problem to the asymptotic version of the scattering process. And then he came to the conclusion the amplitude of the wave function corresponds to the, well, to the, corresponds approximately to the relative frequency of particle intersections at a certain scattering angle theta or a certain position q. In Bo's paper, it's still a little bit confused the concepts of probability and relative frequency which may be pardoned because axiomatization of probability came some years later on. So the wave function somehow corresponds in empirical correspondence to the number of particle sections. And then there is this famous remark of Max Bohm, the guiding field, which is represented by a scalar function psi, spreads according to Schrödinger's differential equation. Energy and momentum, however, are transferred as if corpuscles were really flying around. In a modest interpretation of that statement, you may simply say, well, the dynamic development is described in terms of time, but energy momentum conservation is described in terms of relativistic mathematics of the particles flying around. As if corpuscles were really flying around, you might as if might you read in a little literal sense or in a more hypothetical sense. So, what is beyond the probabilistic interpretation? It was quite good to have the probabilistic interpretation which is the basis of doing physics up to now, of doing

40:00 quantum theory up to now in all corners of quantum physics with all kinds of quantum theory we have today, but no one was content with that, as you know. And it is quite important that we are not frightened of the German interpretation, but it's also quite important to make a clear distinction between Bohm and von Neumann's probabilistic interpretation, or you might say the orthodox interpretation. Von Neumann is simply the generalization of Bohm's probabilistic account to all kinds of observables on the one hand, and on the other hand, the real Copenhagen interpretation invented by Niels Bohr from Copenhagen. And this was account of complementarity presented to us in the famous Como lecture. There are various kinds of complementarity between quantum phenomena, particle phenomena here, wave phenomena there, between particle and wave pictures, and between also the physical quantities that describe the phenomena. And most important, as I picked out here, on the left-hand side, the magnitudes, momentum, and energy, for example, in the Compton effect, which is also mentioned before in this paper, stands for the causal representation. Light quantum gives an energy a kick and decreases his frequency. It's a causal process, which is described in terms of relativistic kinematics for momentum energy conservation. On the other hand, the spatial temporal coordination that cannot be given at the same time. What comes out of Bohr's version of the Copenhagen interpretation is a disunified physics. On the one hand, the measurement methods and the possibility of performing experiments and quantifying quantum phenomena in data analysis in terms of physical magnitudes, there you deal with operational quantities, which are basically classical. If you measure the momentum from a particle track, you take the classical Lohmann's law up to the present day with some quantum corrections nowadays.

42:30 But the theory defines implicitly, in the sense of Riemann's axiomatic method, the axiomatic quantities of quantum mechanics, and both things do not go together, that's a problem. The objects, the so-called quantum objects, who refused the very concept of a quantum object, he said that in quantum physics objects are not definable, they are only indirectly the wave picture or the particle picture of the quantum phenomena. So you have a beam from some kind of source and you have two different experimental devices, a bubble chamber or a crystal, an electron beam. And you have the same kind of cause, an electron beam and two distinct complementary quantum phenomena, here particle tracks and there a diffraction or interference pattern. And the objects are indirectly represented by these quantum phenomena and by the wave picture or particle picture in terms of which they are described. This was made a little bit more explicit by Heisenberg in his 1930 book on quantum theory, the physical principles of quantum mechanics. He spelled this out in terms of analogies and correspondence. I just quote him, It is experimentally certain, only that light sometimes behaves as if it possesses some of the attributes of a particle. But there is no experiment which proves that it possesses all the properties of a particle. Similar statements hold for matter and wave motion. The solution of the difficulty is that the two mental pictures which experiments lead us to form, the one of particles, the other of waves, are both incomplete and have only the validity of analogies analogies taken from the classical cases which are accurate only in limiting cases where the conditions of the limiting cases was correspondence principle in this sense. Heisenberg suggests to apply the wave and particle picture in terms of analogies and correspondence to the classical case and this is

45:00 completely on the lines of Bohr's lecture, even though later Heisenberg's view, other aspects of Heisenberg's views are slightly different from Bohr's. So beyond the probabilistic interpretation there is more than the you who know, and Max Born's statement that I quoted before also may be taken literally and then you come to the concept of a fumes or guiding field and Heisenberg tried to spell this out later in terms of potential Popper tried to spell this out in terms of propensities and Born in terms of the pilot wave. You know that only the of Bohm survived until today. The problem with Heisenberg's and Popper's approaches are that they cannot really deal with the non-local features of quantum mechanics, so to speak with the EPR correlations and so on. However, Bohm's approach of pilot waves is enclosed with special relativity up to the present day, and that's one of the reasons why I do not believe in Bohm's approach, but okay, you know that there is an interpretation of the double-slit experiment in terms of Bohm's pilot waves, which is completely consistent. The problems begin when you switch over from quantum mechanics to relativistic quantum field theory. And then came Einstein in his 1949 replies to the papers on him. much earlier he had said to Heisenberg what can be observed however has to be decided by theory, so Einstein did not accept this gap between the classical operational quantities of quantum physics here and the axiomatic basis and quantum theory itself there. What can be observed has to be decided by theory and not simply by pre-theoretical on the basis of another theory and operational quantities that stand on its own. So he criticized that there is no axiomatic foundation of measurement, and he was looking for a more complete theory,

47:30 and so he somehow suggested that the squared amplitude of the wave function corresponds to an ensemble of particles. He thought that quantum mechanics is only provisional, and always insisted on the search for a better theory. So he came for these reasons of criticizing quantum mechanics as an incomplete theory. He came to an instrumentalistic view of the wave function. That's my interpretation of his remarks, and this is the basis for the so-called ensemble interpretation of quantum mechanics, defended by empiricists like Reinhard Werner from for example in the tradition of the German Ludwig School both share the instrumentalistic view of quantum, of the wave functions and the view that quantum mechanics only applies at the ensemble level and not at the level of individual objects or events so what means a wave particle with this variety of meanings, in quantum mechanics there are the Einstein and de Broglie relations you have light quantum and matter waves and on the other hand there is the probabilistic interpretation and as you all know from this practice both go perfectly together then there is this extension beyond in the authentic interpretation interpretation, there are no waves and there are no real waves there are no real particles but only complementary pictures on the other hand there are realistic interpretations like in terms of both pilot waves and the particles that are guided by these pilot waves or Everett's many worlds approach or collapse theories and so on and so on the main problem on the one hand is their compatibility with relativistic as I said before, and also the ad hoc features that were mentioned also in your talk yesterday. On the other hand, there's instrumentalistic criticism of the wave function, which was

50:00 first expressed perhaps in Einstein's ensemble view, which gave rise to and resist views of the wave function. so now I come to the pragmatic attitude of preparing waves and detecting particles the Nobel Prize winner Wolfgang Ketterle gave a wonderful talk at the annual spring meeting of the German Physical Society in 2003 and he gave a public talk on the Bose-Einstein condensate and then he explained quite frankly to the public It's very hard to understand quantum mechanics, but after several years of physical practice, one gets used to preparing waves and detecting particles. This seems a little bit like how you get used to it. And I mentioned yesterday in my talk with you the SUAC interpretation of quantum mechanics, shut up and calculate. this is not this pragmatic approach is not really to be reduced to this kind instrumentalistic dealing with theory but it is really based on physical practice on experience physicists make in the labs there are many physicists overall in particle physics whom I know who defend that they prepare waves and so on, and they detect particles finally. And the philosophically interesting point here is that preparation and detection are asymmetric, empirical procedures or experimental procedures. They are not really on a path. And there's almost no literature, I know, that takes this point up. And I'd be grateful if someone knows some book or article who is about that. The preparation of a quantum state usually is made as a momentum state. For matter, in the experiments of high energy physics, the accelerator prepares a particle beam of a ratified momentum. On the other hand, in the experiments of quantum optics with light, one usually prepares monochromatic light of energy

52:30 a very small dispersion of the wavelength of frequency. Why is preparation usually made as momentum states? Because in quantum mechanics there is this well known dispersion of localized states and in quantum field theory there are no localized photon states at all. according to quantum field theory with photons, with light, one is always forced to work this momentum state. And then different types of momentum states are generated with different properties as regards the relation of phase and amplitude. On the other hand, the measurement of a quantum state is usually made by a particle detector. This is true already for the famous Stern-Gernach experiment. beam, electron beam, and then you get two spots. In high energy physics or particle physics, a matter is investigated by position measurements and their sequences. There are similar spots on a photographic plate, there are particle tracks, there are scattering events. Light, on the other hand, is measured, low energy light, low intensity light coming from a laser, it counts in a photodetector, a photomultiplier also. And this works as this is basically the absorption of a photon account in a photodetector. Why are measurements usually made by a particle detector? Because measurements are performed locally in a physics lab and it rewards the spatial temporal information as a basis for data analysis. So, preparation and detection are asymmetric. Quantum mechanics and quantum field theory, in a certain sense, that I tried to explain before, they prefer momentum states, and experiments, on the other hand, aim at comparing stable reproducible states. Stable reproducible states are momentum states. On the other hand, to detect particles of a well-defined mass charge and spin, within a very small space-time region.

55:00 This is the aim of all the work with particle detectors. So the waves propagate through the apparatus in the experiments of particles. But finally particles are detected. What remains here of the traditional classical particle concept concept. A particle is something like a collection of dynamic magnitudes, mass or energy, spin, parity, and various kinds of charges, the electric charge, but also the charges of the other interactions, four flavors, four colors. And a particle is a collection of dynamic magnitudes that is localized in an experiment. It has to be noted, this operational particle concept has a feature that virtual particles fall out. According to my view, they do not really belong to the particle family. They are something like the black sheep of the particle family. On the other hand, the quarks localized within the nucleus by scattering experiments can be defended that they still fall under this operational particle concept, but I cannot go into these details here. On the other hand, there are conservation laws and the conservation laws describe the propagation of a wave. So there's a particle track on a photographic plate and there's a sequence of positional measurements and one assumes that along the track charge and mass of the electron have been conserved and the energy as well. On the other hand this operational particle concept is a collection of dynamic magnitudes that propagate through the detector according to the world or through the operators or through the universe if you generalize it. This according This operational particle concept is in relation to Wigner's particle definition that already was mentioned yesterday.

57:30 I put here a question mark and an exclamation mark. On the one hand, it's a postulate that the operational particle concept corresponds to Wigner's definition. On the other hand, as I already said yesterday in the discussion, Wigner's particle definition does not really come down to earth from the group theoretical account of particles, no single localization in a particle detector, such a collection of dynamic magnitudes may be derived and that is therefore the question mark now I come to recent which way experiments in quantum optics they are experiments with single photons and atoms the famous experiments with single photons has been performed in between. It was already suggested by Einstein in his famous discussions with Bohr and it was a thought experiment Heisenberg and for Feynman to measure through which slit the particle may pass. The double slit experiment is a very nice example of the propagation of a wave through the detector but the detection of single particles finally at the screen and obviously here you have wave particle duality in one experiment so at this point one should also be clear that Bohr's approach is too narrow and it should be generalized generalized. Another kind of experimental device is a Mach-Zehnder interferometer. They work with two beam splitters and a phase shifter in order to generate interference of two partial beams. This also made part of the reality in one experiment. Then there was a famous paper of Scalby England at Walter in 1991, they suggested in the tradition of these thought experiments I mentioned before, measuring through which of the two slit the particle passes, they suggested to prepare atoms, so now I need to show something.

1:00:00 Do you have a laser pointer? So, here comes an atom, an atomic beam, and there is a laser, and the atom is excited, and then it passes through the double slit. Behind the double slit, there are two cavities, and the dimensions of the experiment are such that within one of those cavities, the atom will decay. So after the atom is passed, double slit, only without cavities, you would expect an interference pattern. But the prediction of Scully and so on is that if the photon is deposited in one of the cavities, then the interference pattern is destroyed because course this is a path, the path has been marked, and they also predicted that it is sufficient to store the information within the cavity in order to destroy interference, but it's not necessary to read this information out. There is no observer needed to look, and no where the photo really is. It is official.