Transcendental Philosophy & Quantum Theory — Part 2

0:00 It is Reichenbach who applies the double language model in the specific case of accounting theory. Similar to Kahn, Reichenbach considered that in the case of accounting mechanics, the vocabulary, the O, or observation of terms, is defined in relation to measuring process. We have an observational language and a quantum mechanic language. The observational language contains terms such as Geiger counter, Wilson cloth chamber, black line on a photographic film, indication of the dial, etc. The phrases margin of U and the result of the margin of U are defined in terms of these elementary expressions. Similarly, a physical situation S can be defined in the observation of terms. The quantum mechanical language contains terms like position Q of an electron and momentum P of an electron. Between the two languages, there exists the following relation. The truth and falsehood of statements of the quantum mechanical language is defined in terms of the truth and falsehood of statements of the observational language. We say, for instance, the electron has the position Q, when you know that the statement, a margin of position has been made and its result was Q, is true. For Heschenbach, the meaning of the quantum mechanical statements are based on the meanings of the observational terms, and without this definition of meaning, it will never be possible to establish the language of quantum mechanics. We know that Carnapis-Reichenbach's semantic model about the theoretical observation of scientific concepts was harshly criticized by among others, Hansen, Feyerabend, Putnam, Gore-Martin. Each of them, in his own way, argues against the possibility of drawing a line between observational and theoretical terms.

2:30 However, the language problem stirred up by quantum mechanics has not been especially addressed either in Carnap's anti-realistic approach or in other anti-realistic approaches, such as those supported by Roman Maxwell and Hilary Kutner. No account at all has been taken concerning the paradox of the linguistic limitation in the micro-physical realm. Both approaches fail to make a distinction between the theoretical terms used in the language framework of classical physics and those using the quantum mechanics. There is the same semantic model, which is valid for terms that define natural kinds, such as those defining biological species. for terms applicable to the unobservables. Terms such arthropods and chromosome are treated in the very same way as electron, positron, and spin. Even Putnam did not pay particular attention to the specificity of terms attributed to the unobservables, even though he concerned himself with the logic of quantum mechanics and with criticism of the Carnapian distinction between observational and theoretical terms. So, let us take examples, two theoretical terms, chromosome and electron, and let us look up the respective meanings in our dictionary. We'll find, for instance, the following The homosome, the microscopic, thread-like part of the cell that carries hereditary information in the form of tubes. And electrons, one of the constituted elementary particles of an atom. Under normal circumstances, electrons move about the nucleus of an atom in orbitals that form an electric cloud bound in very strengthening and positively charred

5:00 meters. Those for whom quantum mechanics does not constitute a problem may think that both terms have very similar linguist and epistemological features. Both derive from and have their established within contemporary scientific theories, biology and physics, respectively. Both are parts that constitute matter, the cells for living creatures and the atom for all beings. However, if biologists, on the other hand, on one hand, could readily accept the correctness of the first definition, the quantum physics could hardly accept the second definition. Let us suppose that the editors of a particular dictionary for the course of issuing a new edition request the community of quantum physicists physicists to define the word electron in the most exact way possible and to reflect the applicable state-of-the-art knowledge. The physicists will find themselves in the awkward position of having to concede that, unfortunately, any definitions of the word electron that they could provide in ordinary language would be full of ambiguities. Some of these physicists would go even further and risk saying that such a word could in no way be defined on a final basis. Physicists are normally tolerant of the ambiguity of dictionary definitions of terms used in atomic theory, and they They concede that this ambiguity is itself part of the very nature of their knowledge. Philosophies of language carry on as if both definitions had the same semantic status.

7:30 With Carnarv, the means of these two theoretical words, chromosome and electron, may be established through some kind of correspondence between them and observational terms. If, on the one hand, we accept that the criticism of Hanson, Hayard, Button, and Maxwell really dissolves the problem concerning the distinction between theoretical and observational terms related to any scientific theory, on the other hand, we have to consider that the distinction between quantum physics vocabulary and classical vocabulary still remains a problem. In my opinion, the solution to this problem cannot be found in terms of a semantic analysis of language, but rather in terms of a pragmatic approach. In order to analyze the conditions of possibility to say something significant, in ordinary our language about the inobservables, we must now turn to the pragmatic transcendental perspective. We thus realize how far removed Carnot's double-minilanguage theory is from Bohr's complementary interpretation. This letter presupposes that the term electron, that that exists a pragmatic interpretation of complementary descriptions, rather than a partial semantic interpretation, as we have in Carnap's approach. The solution found by Bohr was to limit in a complementary way the use of concepts, renounce the realistic ideal of producing space-time descriptions of the micro-physical reality with a framework of a predicative semantics. If physicists still use space-time descriptions containing classical terms, they do so for pragmatic reasons. They must communicate their experiment results, and to do so, they must use ordinary language. None of the complementary descriptions in terms of wave and particle is compatible with a theory of reference that presuppose

10:00 a microscopic reality of inobservable objects. The contradictions is applied by consider the formalism inconsistent in itself and with which contradictory empirical description. We are facing a case of reversed Durheim Quine thesis of under-determination of theories by the empirical data. It's not a matter of conflicting theoretical system same empirical situation, but rather on conflicting experimental situations with the same theoretical formality. The contradiction appears when we try to include in one single interpretation both formalism and more than one case of experimental application, as if they refer to the some inobservable reality. The only way to avoid ambiguity is to impose upon it a limitation in terms of the pragmatic use of concepts from the ordinary language. I am of the opinion that the deep sense of Bohr's interpretation presents an approach that is, at the same time, pragmatic and transcendental. A further step should be taken towards the pragmatization of the ethereum in order to take into account the performative dimension of language. With Bohr, we had to admit the fact that the conditions required for understanding a physical phenomenon are, at the same time, the conditions of the very possibility of communication. In my opinion, this performative dimension, sometimes overlooked in the epistemological analysis, proves helpful in an attempt to interpret the complementary role of theoretical concepts in experimental context of quantum mechanics. However, I add that the meaning of a proposition cannot be grasped independently from the contextual value of the proposition itself. The pragmatic transcendental turn, taken by contemporary philosophy, start by Wittgenstein, points to fact that in

12:30 order to understand certain propositions, the context in which they are made is a determinant of their meaning. Should we take the ordinary language as a part of a game also played by quantum physicists as they communicate experimental results, we would be in a better position to understand the role it plays in the very definition of quantum objectivity. This objectivity is no longer subjectively determined by a universal conscience, as claimed by Kant, but rather intersubjectively limited by experimental context which should always be communicated. I believe that such perspective has important implications in terms of ensure both a good interpretation of quantum mechanics and the development of a sound theory of science. But what exactly is the novelty introduced by this pragmatic transcendental approach? In a constitutive level the physical knowledge of the world contextually dependent upon the conditions of observation aims at reconstruction phenomena with their logical mathematical structure. However, this logical mathematical rationality does not suffice. It always presumes the existence of the discursive level, that is to say, the level of ordinary language in the light of which the experimental performance are described. These two kinds of rationality, mathematical and distance, must be considered as parts of an interpretation process where merely formal symbols are related to ordinary concepts, which are simultaneously subordinated to the experimental act of measuring and to that of communication. Thus, new transcendental principles must be found not only in the constitutive level of experience

15:00 but also in the performative level where the constitutive statement will ensure an intersubjective agreement. From a pragmatically transcendental perspective it's no longer matter to think that phenomenal objectivity is caused by an unobservable reality even if such reality are known or hidden. It is time to seriously stake into account the necessary intersubjective character of objectivity for which a pragmatic perspective is required. The highest principle of all synthetic aprioric judgments may be reward from a Bohrian point as follows. The conditions of the possibility of experience in general are likewise conditions of possibility of an inambiguous communication of the results of experience, and that for this reason they have objective validity in a priori propositions. The objectivity of experience, therefore can be understood in the sense that it may be shared in an intersubjective way. Quantum mechanics is the best example of the performative act according to which the statements used to communicate experience are themselves actions. Michel Bittable's interpretation of quantum theory has led us to consider that the mathematical rationality of formalism cannot be detached from our condition of beings acting in the world. We now have a wider picture of the different a priori dimensions. The pragmatic transcendental perspective led us to consider at least three such dimensions. That of the a priori as constitutive principles of quantum objectivity, mathematical and dynamical dimension, that of the a priori as regulative principle of quantum theory, ontological dimension, and that of a priori as performative principles

17:30 of communicative and experimental activity, pragmatic dimension. However, these three dimensions are not quite so independent from one another as they integrate in order that they may constitute the field of validation of our scientific practice. The constitutive and regulative apriori dimension of experience is in quantum mechanics inexorably attached to the apriori dimension of communication, which assumes that ordinary language plays a special role. So, thank you, Patricia, for this very interesting talk. I see several, I don't even know who was the first, Alexei. Well, I looked up the definitions of Electra. Ah, okay. So they have good definitions, I would say. They have a, well, Oxford English Dictionary does very bad. It defines electron in terms of the proton and proton in terms of the electron. But other dictionaries do pretty well. They say that electron is a lepton with such and such mass and such and such rest mass and such and such charge. And this seems to be something which we can say today, and this would be basically ordinary language for us today. which was totally inaccessible in 1930s because no one knew what leptin is. You know, the word didn't exist. So, yeah, but what is happening is something which a dictionary can still state today. You know, this definition was simply impossible in 1930s. Total, completely impossible. It's still possible today for at least those, you know, in dictionaries and can look up leptin and do further on. So there is no need to refer... Particles such as electrons. No, well, I'm not sure. Anyway, but the thing is that something you have actually mentioned, that the tendency in which terms of technical,

20:00 of the scientific language, moving to the ordinary language changes completely the whole landscape. Means that something which for Carnap in 1931 was absolutely necessary, he couldn't imagine a definition of an elementary particle of an electron other than by means of traces in a chamber. Today, we can do without. So that seems to be a way out of that problem. Because what is it exactly? comment on that as a Bohr expert and as a former experimentalist in physics and I think that Bohr produces a lot of misunderstandings by putting into the same box ordinary language what you find in the dictionaries the dictionary definition here is a great school teaching about atomic physics on the one hand on the other hand the language of classical physics where we are which It contains concepts as a mass charge, position, momentum. And this has to be distinguished. And then I think the whole picture is a bit different. And the dictionary definitions refer to terms that should refer. But quantum physics has this big reference problem that is not resolved. and this is due to the Heusendag's ensemble relation and because the objects don't have position at momentum at the same time. I don't know because I don't think well I think there is I certainly think that there needs to be a lot I agree when you're saying when Bohr was using the term classical language and he didn't really differentiate enough because you know we have to be to be much more precise about what we mean by these different languages. But I still think that the argument stands what used to be believed not to belong to the ordinary language with the way science proceeds starts to belong to it. the definition the boring approach in terms of language is something which is evolving in time and it's clear how much of a universal status this can have I think that Gordon makes

22:30 this distinction between an ordinary language and classical concepts but he He knows. He should have. He should have. But he knows that. He won't know that. He knows this problem, but he knows good is the definition. Because for him, he knows that the classical physics and the ordinary language may use a natural semantics of the things that have reference. and it's the same semantic to classical physics and ordinary language but the concepts are not the same but for him it's not a problem because what's it's taking place in quantum mechanics concepts that don't have this semantic I just wanted to just follow up on what Alexei said, he asked a physicist The definition of a particle is simply look up the particle data booklet that has all the information that a physicist would ever want to have about a particle. Yes, that's right. There's this little thing that is edited every year by someone. Yes, but the problem that was raised by Patricia is how do you obtain this data? You have to apply on the background, which is a practical background, a background of experiment. And that this whole set of elements cannot be synthesized in such a way that you can refer in the ordinary way. So it's really... Yeah, so who was next? I'm not sure what you said, because you're reading the horror, and I have sensed this sort of content thing in the horror too, and it's been one of the things that I sort of didn't like is that he was sort of sticking to ordinary language and accepting all these restrictions on how ordinary language he allows to express things and trying to put these behind all the

25:00 but I'm not so sure that I would agree about all this ordinary language that experimentalists use to describe their experiments because when I talk to experimentalists, and I know that the philosophers often make a big point pointing out things like this, and experiments are very late in some sense. They'll use terms, like, well, we get the new sub-dopper cooling, or, yeah, we're going to use electromagnetically reduced transparency in order to, you know, cause this effect. And some of these things, like EIT, is already taking advantage of quantum coherence between two different states in some atom, you know, in order to get other effects. So, you know, I'm almost worried that the ordinary language one has to use is getting to the point where one is going to have quantum concepts right in there describing what one is doing. And, you know, 30 or 50 years, just like, if you want to use dye laser at more than 50 nanometers or something as an ordinary language concept, in 30 or 50 years, you might have on a computer as a ordinary language concept. And I'm just not sure where that kind of ordinary would be. The problem is... we can't speak of ordinary language, but how we can describe a specific experimental situation without using natural semantics, that's the problem. Not with the concept of ordinary language, Because when words tell about ordinary language, it is to tell about the concepts that we utilize in a natural way, and to specify the results of experience, and you analyze, for example, the frames of interference, you...

27:30 In a pragmatic way, not in a, the physicists know that he can't explain that in a realistic way, but usually he used the wave picture. Just an example of this one phrase, here's an example, here's an example of what will happen. will say, first mommy, then daddy, then I'm your superposition. This is ordinary language and this is the language of quantum mechanics. Do you have a child that does that? No, no, no, I said we'll say, I said we'll say. But this is, this is what Ferrit is talking about. Well, I, I want to try to follow up on this, the same line of thought. I mean, I, I think the point Brigitte first made that Bohr's idea really is its classical mechanics, not ordinary language, you know, is very, very important. And in particular, you know, if we're going to look inside the atom, we have to use classical waves. We have no other way that the spectra is all about. So, of course, what happens inside the atom, we can't describe classically. To get in there, we have to be classical. So, this is a point that has been made already. Now, but let me, what do you, when you talk about transcendental pragmatic and pragmatic transcendental are you are you alluding to Habermas in any way by those terms? Oh, I read Habermas saying that this because, but Habermas it used transcendental pragmatic transcendental in the and conditions of communicative rationality transcendental pragmatic conditions and the communicative rationality. Is that the kind of context? But in the ethics, but not in the epistemological, I think. But there is a happiness inspiration here. Well, but then there's some other kind of gap, because Habermas makes a big deal of distinguishing communicative rationality in this transcendental, performative, pragmatic sense from instrumental rationality, which he takes to be paradigmatically exemplified by scientific knowledge, mathematical scientific knowledge used instrumentally.

30:00 So he doesn't take scientific knowledge to be a realm of communicative rationality at all, but a realm of instrumental rationality. So it really is ordinary language that is as opposed to even classical mechanics. Of course, I think he's wrong about that. I would say the scientific language is a paradigm of communicative rationality. And I would think Bohr, if he met Habermas, would say classical mechanics is a necessary condition for communicative rationality. But then, why classical mechanics? Especially if we take account of this change of language and practice idea that people have been using. to get at that idea would be to say, well, no, there really is some, you know, quote-unquote real Kantian stuff there. Something about space and time, something about causality as themselves conditions for this kind of rationality. And classical mechanics, you know, paradigmatically puts together space, time, and causality in a unified and coherent way. And what the problem with quantum mechanics is, it doesn't do that. So that wouldn't just be appealing to ordinary language or Habermasian communication, it would be adding some further Kantian idea about the privileged position of space-time and causality, or perhaps a Husserlian idea about intuitive space, intuitive time, and intuitive regularity. So somehow these things have to... Yes. No, I agree with you, because Habermas don't use the context of knowledge and scientific knowledge. It's instrumentalist in the way, but for the philosophy of science, the problem of the intersubjectivity and the necessary community what we agree in sense of the regulative principles too that's not the constitutive principles but the regulative principles it plays a role

32:30 that's very very important that we we have to consider a community of scientists and it's it's because i don't mention happiness because we are very it's an inspiration but we are very far from yeah my question is quite the same You use the term pragmatism in many different sense, meaning, you use it in the Wittgensteinian sense, you use it in the communication sense of the pattern, you use it in the linguistic sense as opposed to the current sense of the language. But in that case, where is a characteristic of pragmatics in the sense, as opposed to semantics, maybe lexicality, these problems of indexical patterns, etc. And in fact, we lose also it in relation with performative, the performative, so sense of performative language. So I need some clarification. I think you might. And there is also the Bersian sense, pragmatism, pragmatism, which is directly transcendent, explicitly a sort of reformulation of . And Michel is also a Bershwin. Yes, but I use, I have in mind the Charles Moritz characterization of only the characterization of synthetic approach, semantic approach, and pragmatic approach. in the sense of pragmatic approach we have to consider the community and the language to establish our meaning in the sense very very wide and the reason

35:00 we have reason to say that we have to precise because in this wider size we we can put together very different conceptions of pragmatics and English and performative ways of thinking. It's a problem. I think that's a problem. May I make another remark on Bohr? I don't agree with the fact that the transcendental aspect of Bohr concerns the problem of thinking ordinary language with formalism, and quantum formalism with the definition of the science and the sense of character. For me, the transcendentalism of Bohr is, first, reduction to observance, only observance, and secondly, we are able to reach a strong concept of objectivity, That is, without any ontological commitment. And for me, this is the transcendental aspect. The disjunction between ontology and ophthalmology. If I have reason, because when I take in mind three dimensions, And I would like to show that we have this constitutive dimension in Borough, but we have to, I would like to show the pragmatical dimension of the communication. We can walk together. So you have had a question. Yes, but it's been asked already several times. I just wanted to remark that sometimes this is a lot important to them. You want to create terms like filling up on the term, I wish to comment about one of the points of Jean's when you asked about the possibility that indexical

37:30 interviewees, which is very important to the dimension of the practice of language I think in some way you can point out the connection between indexicals and what has been called by some authors latent indexicals. For instance, when you say I or now, you directly point towards a certain point of view. But when you just say, oh, the sky is blue, it looks like you have not any indexical component in it, That means that you are referring to something from the Earth in this situation, which is particular to me. I completely agree with the indexical aspect. So I think in the same way, when you are speaking the ordinary language enriched with classical concepts, You are implicitly using an indexical point of view, which is the point of view of human beings in the macroscopical environment. So I think this is a pragmatic diagnosis. An experiment and interpreting it. So thank you very much. Thank you. Yes, I seem like it's been around everyone. Sure. One problem also with talking about the community is the community of experimental physicists very quickly will just bring all these technical concepts, including quantum theories, into that their description of what they're doing is they will have no problem. Rational communication.

40:00 But still, that doesn't solve the problem. That doesn't solve the problem. Do you think, was it right when I said, do you think that it really has more to do with how do you put space, time, and causality together? I mean, it really has to do with this original concept. But Bohr has a very use of the word intuition. Sometimes he also says that so he doesn't make the distinction between the concept and his neocentia. But at least he thinks space, time, and causality are fundamental. Classical physics embodied them in a coherent way. The fun mechanics have pulled them apart in complementary way. as a part of the same. This gives a very clear criterion of separation between words which refers to other words which refers to something completely different. For instance, when all the people say, oh, entanglement could be a word of the ordinary language. No, in the sense, right, indicating it can be. But they might, we have to distinguish. and they might, in the lab, start talking about entanglement and who knows what else, but still what we want to say, as philosophers looking at it, there's something called the real language of the lab, which has more to do with what you actually see and do with these machines. There are many informal terms, like Harting-Lang-Electron, and on the other hand there are the observables, is the concepts of classic properties that can be measured. And in the philosophy discussion, there's a lot of confusion about these distinctions. Also about the term observable, about the difference between observation and measurement. Einstein's guilty of that. And yes, and observable is not what can be observed by, But how do we look at the laboratory and what language do we want to attribute to the experimentalists so that when they start talking this talk, they're saying, well, that's not really what we mean. We mean the language of actually dealing with this stuff. What more can we say?

42:30 It's very hard. I'm a home experimenter. It's very hard to communicate this way of talking to my philosopher colleagues. It's very hard, and then most of the people do not be interested in that. It's really a hard job. But how do you, how would you, you know, so how would you characterize the language of the experiment? Well, on the one hand, it has several levels, including the concept of quantities, of magnitudes that may be measured, mathematical concepts, informal terms that talk about electrons as if they were entities to which we may refer in a class presence. and physicists usually are quite unconscious of these distinctions. And on the other hand, they permanently make use, tasted use, of course, correspondence principle, which has nothing to do with counter-correspondence. Right, right. It's an inter-theoretical relation. Right, right, right. And so was absolutely right up to the present day from my point of view that quantum theory, quantum mechanics, quantum electrodynamics, and so on, are abstract symbolic formalisms without any physical interpretation. And the language of physical magnitudes or physical quantities is almost neglected in the philosophy of physics, and this is the very basis of... Certainly, this is such a measurable magnitude. Yes, this is the very basis of interpreting the formalism. measurable magnitude Yes, and then the theory, the observation shift with time. And that's something very broadly. Oh, she was in power. Yes, yes. Do you really want to say that the abstract formalism with no physical interpretation? This is pure mathematics. It's a physical theory. No, physical theory, the mathematics, it's Hilbert's-based humanism.

45:00 Again, from mathematics to the physical theory, it's very large dimensions. Okay, okay. And this point is absolutely neglected. Okay, so that's another important point. And that's the basis of defined magnetism. Just to explain the title briefly, the inflammation part of the talk has to do with the claim that And the decision from classical economy planning is something to do about information, information in the physical sense, that is Shannon's sense. And the objectivity part of the paper has to do with how one should understand the measurement problem in the light of the claim about information. So I want to start off with a game that I'm going to call the Pesco-Rolish game. and it involves also Bob, so we need to get an iconic Alice and an iconic Bob and a moderator. So, I just learned how to do this, so it's not for this slide, but the others are sort of less bad stuff. Anyway, the game works this way. The moderator sends a zero or a one, two Alice and Bob separately. Alice and Bob can agree on a strategy before they start the game and then they have to separate. And they can't communicate after that. And when Alice gets a zero or a one and Bob gets a zero or a one, you can think of them as being in such a television game show and they're in two different rooms. They come through beforehand, they go to their rooms, and they each get a zero or a one. And they have to respond with a zero or a one. They win the game if the boolean sum of their responses is the product of the bits that they get sent. Now, what that means is just that if they get sent bits, pairs of bits, independently, such that the product is zero, which means that in these three cases, 0, 0, 0, 1, or 1, 0,

47:30 they have to respond with a pair of numbers, pair of bits, where the Boolean sum is 0, which means it has to be 0, 0, or 1, 1, which means that they have to respond same in these three cases, with the same thing. And in this remaining case, they have to respond with different bits. Okay, so there are three cases where they have to respond the same, and there's one case where they have to respond with different bits. Now, it's easy to see that the probability of winning the game, winning the game means responding correctly in that fashion, is that there are four possibilities for the pairs of bits that they get set. That's the quarter, so the probability of same given that they get zero, zero, That's probably the same if they get zero to one, so that's probably different if they get the one in that case. So here I've just changed the annotation to connect it up with the Clauser-Hohn-2-1-Holt inequality. We usually have two measurements of this particle, two measurements of that particle, and the measurements here, the observables measured here are A and A prime and B and B prime. So this is exactly the same thing, just for that change of notation. And this sum of probabilities is very easily related to this expression in the Clauser-Horn-Humonti-Kolk inequality, the expectation value of AB plus AB prime and so on. Because this is just the probability of same minus the probability of different. The probability of different is one minus twice the probability of same. to this K lambda. So the probability of winning the game is just half plus K over 8. Classically then, by the Klauser-Horn, by the valley inequality, the Klauser-Horn-Schuhn-Schuhn-Schultz inequality, the house cannot win the game with a greater probability than three quarters. That's the possible situation. And it's easy to see what strategy they should employ to win the game with probability three quarters. They could just decide beforehand to always respond with a zero or a one for that many.

50:00 So they both respond zero no matter what the input is. If they always respond zero no matter what the input is, they will win three quarters of the time. So that would be a simple strategy if you don't require that, you know, further condition that they have to come up with zero or one half the time. So that would be a simple strategy. And the Klauser-Horn-Chimonie-Holte inequality is essentially a proof that that's the optimal strategy, classically. On the other hand, if Alice and Bob are allowed to take into these rooms where they play the game, Stern-Gerlach apparatuses, quantum measuring apparatuses, and beforehand they're allowed to prepare lots of entangled pairs of particles in a single state, and they can take with them each a bag of particles labeled in secrets if they're going to play the game, let's say, a hundred times. All I need to do to win the game with a greater probability than three-quarters is to make spin measurements on their individual particles in a certain correlated way. In fact, if Alice gets a zero, she measures spin in the z direction. If she gets a one, she measures spin in the x direction. And Bob does the same thing, but rotated 135 degrees. And then they win the game with 85%. So, this is really very strange because both classical mechanics, let me just go back just to introduce a bit of terminology. I mean, this idea comes from Capescu and Rawley in an early paper, actually, in the late 80s. But it's clear that classically the other bound is 2, quantum alpha bound is 2 root 2, but it's possible to win the game every single time. and it's logically possible, you could just sort of guess randomly enough. And in that case, you would saturate this inequality so the boundary would be full. So, and in the case where you win the game every single time, 100% of the time, Professor and Raleigh can produce non-local boxes for these devices. They're still taking correlated pairs of particles in the rooms,

52:30 you would have in this hypothetical universe where you could win the game 100% of the time, boxes, and you would just input a 0 or 1 into a box. It would output a 0 or a 1, and that would be the number to use, and that would always correlate in the right way 100% of the time. Now, all these theories, classical mechanics, quantum mechanics, and non-local box theories, hypothetical theories, they all satisfy a no-signaling condition. The no-signal condition is not exactly a relativistic condition, although if it were violated, you would be able to signal super-bloomally. But all it says is that the probability of outcomes on the left, and here it uses A-B notation instead of 0-1, which finds the fact that it's Alice or Bob. So A and A-prime for Alice and B and B-prime for Bob, the probability of Alice's outcomes is independent of what is being measured on Bob's side. So there's no way that Alice can see any change in his statistics that Bob has actually made a D-measurement or a D-prime measure, or in fact any measure before. So all these theories satisfy no signaling condition. So this raises the question, why quantum mechanics? I mean, why do we live in a quantum world and we say, why can we win the game with 85% of the probability and not, and we are not confined to 75% of the probability? Given that, there's no conflict with any signaling condition. And it's like, why can't we win the game all the time? Why can't we construct a couple of boxes? There's no violation of those signaling or logic in any of these cases. Here's a quote from Feynman. Some people always quote where he says that there are no reason to understand quantum mechanics. Don't keep saying to yourself that you can possibly avoid it, but you can't be happy to be like that. Because we'll get down the drain into a blind alley from which nobody's here to skate and no one knows how it could be like that. And he contrasts that with the theory of relativity where he says, you know, everybody understood the theory of relativity in the beginning. So, what is it about quantum mechanics that as opposed to the theory of relativity? We've heard a lot about theory of relativity. that raises a special problem of the ability. We want an answer to why quantum mechanics

55:00 and not classical mechanics, and why quantum mechanics and not theories with super correlations like the non-local box theory. We want to ask the question why quantum mechanics in two senses, why quantum are not classical and why quantum are not super quantum. And we want an answer to that question that's illuminating which they define That is, you want some principle and strength that allows us to do something, and it's impossible classically. It's impossible classically to win the game greater than 75 percent of the time. And that's a puzzling thing. Okay, so let me mention this one more interesting thing. This comes from a paper by Toner and Fitzgerald. And it's a diagram which indicates another difference between the classical situation and the quantum and the non-local box situation. The classical correlations are what you might call polygamous. That is, this is the correlation between Alice and Bob, and this is the correlation between Alice and somebody else, Charles, let's say. Now, this box here, with the maximum value 2 here, the bounds 2 and minus 2, show you that you can have, you can be maximally correlated, or optimally correlated, at least maximally correlated, with, how else can be maximally correlated with Bob and at the same time maximally correlated with Charles. But this circle gives you the quantum region And you can see that if you're at the 2 root 2 value for Charles, then you're at the zero value for Bob, sorry. Then you're at zero correlation with Charles. You could have a correlation of 2 with Bob and also Charles, but you can't have 2 root 2 with Bob and Charles. And similarly with these non-local box theories, where you have a maximum of 4, if you give maximum value of Paul as well, then it's zero with Charles. And this has an important application to the point of cryptography, because if Alice and Bob are correlated to the maximum, then you know that nobody else, no other Charles, can have a similar correlation.

57:30 And that can be exploited in a way where Alice and Bob can have a secret key which no Charles can have access to. And you're guaranteed by the laws of physics if that's the case. So that's another feature of these correlations that we should try and explain. So let me move to special relativity and go back to the comparison of quantum mechanics. Special relativity, I would say that, in fact, I mean, I think we've seen this here, the surprising and salient discovery leading to special relativity was the discovery about light, that light as a, in the blonde ecosystem, there would take a light. It's independent of the loss of the source, and special relativity is the revision of the conceptual framework of possible mechanics that stems from Einstein's recognition of the foundational significance of the light possible. Now, I want to argue that the same surprising discovery unlike quantum mechanics is that there's a limitation on copying information. But our world is the sort of world in which there doesn't exist a copying machine that will flow in the outputs of an arbitrary information source. More precisely, there are information sources that can't be broadcast. I'm going to use it with cloning, but I'm actually talking about broadcasts. Cloning is a more familiar word, so obviously. And automechanics is the revised conceptual framework for mechanics that stems from the recognition of the foundational significance of this fact and the cloning principle. Let me just say a couple of things about Einstein versus Lorenz because Lorenz had a different explanation for what is puzzling about the light posture or how to reconcile the light postulate with the relativity risk. The behavior of light for Lorentz is explained as a dynamical effect of the ether of rots and quads. And these are the light for the physical of relativity or reconciling the framework of Newtonian mechanics of absolute simultaneity. Certainly I want to argue later on that there are what I want to call Lorentzian, I mean I'm going We use a sort of good jar of sense. Lorentzian interpretation is part of the mechanics, both, Everett, beyond W. And they, what these interpretations are doing is that they're solving the management problem

1:00:00 by proposing what is, in effect, a dynamical explanation for no cloning. And in that sense, they're Lorentzian. Okay, so what is this no cloning principle? Let me formulate it inside. No cloning principle is simply the principle that there's no universal cloning machine. I'm not going to say exactly what I mean by cloning machine, but the principle is that it's impossible to construct a cloning machine that will clone the output of an output information source. And it's a principle like the principle that there are no potential motion machines. Note that by contrast, you can't have a universal computing machine if you can't have a universal So what's the universal cloning machine? Well, the universal cloning machine I'm going to define as follows. Given an arbitrary information source X, the next transparency will have a picture so you can see. Producing outputs PI with probabilities PI, because that's what an information source is. It produces outputs with probabilities. The universal cloning machine is a device that you could couple to S. source, where the outputs of S are input to this device. So the compound device is now a new information source, S star, that produces outputs, Fi, with the same probabilities, where each Fi consists of the original output and a copy. And what do I mean by a copy? Well, a copy is an output, a copy of Ei, or a copy Ei star, that conveys the same information as Ei. that the information source PIEI star is statistically distinguishable from the information source PI by PIEI by prospect measure. Now, let me just mention here that, again, I'm talking about broadcasting really, the process of taking a probability distribution to a new probability distribution over a product space where the marginal probabilities are the same as the originals is called broadcasting, and that's really what I'm talking about, but I'm cloning the purest states of your life. But I'll use the term cloning rather than broadcasting because that's more familiar. So, now, and I also, just a side remark, there's no cloning

1:02:30 principle for quantum mechanics, which is explicitly recognized in the 80s, so you might say this is really very very strange to sort of claim that this is the principle underlying quantum mechanics too but the whole debate between Einstein, Schrodinger, and Bohr, Heisenberg, Pauli and the others ultimately I would argue have to do with features of quantum measurement that are puzzling just because of the conflict between the no-cloning principle and the conceptual And there's all framework, classic . And so it .