The collapse of the wave packet (contd.)

0:00 And I'm explaining this in terms of the correlation at this earlier time. So, and this is by a standard V-N explanation, deductive nomological explanation because we have straight deduction from here to here using passivity. But we can do better than that. It's just saying that there's a formal derivation there, and hence it's deducted nomological explanation. It's not a very exciting form of explanation. We can make this, then, quite a usual form of explanation, a causal explanation, because what we have is, in fact, a simple two-step causal process. A simple two-step causal process for explaining the Cartwright correlation. And it looks like this. The first packet sets up a correlation between s y positive and z plus one. Notice however that that correlation is not the same as the collapse of the wave packet. This is a much weaker statement than the collapse of the wave packet. It's a correlation, alright, and it's a correlation which is implied by the collapse of the wave packet. But it's not itself equivalent to the collapse of the wave factor. It's a weaker assumption. It's just a correlation between possessed values. It doesn't say that you get off-diagonal terms rubbed out by the measurement interaction. It's a very weak correlation claim, which is in fact derived from the existence of this later correlation, the Cartwright correlation. So the initial measurement sets up a correlation between these two. That's the first step. And that's a purely causal process. The second part of the causal process, the measurement M2 correlates Sy positive Z plus 2, and that simply gives us the measurement as passive. In other words, Sy positive causes, in the measurement interaction, the second magnet to make a deflection upwards. So a purely causal process. And when you combine these two, if you think about it, here you've got that correlated with that, here you've got this correlated with that, so therefore, of course, that's the derivation that I've done, this follows, therefore, hence Z plus 1 is correlated Z plus 2.

2:30 That follows from here and here, it follows that this occurs, and this is our hard drive correlation that we require to explain. So we've explained the Cartwright correlation not by the collapse of the wave packet, but essentially by assuming the Cartwright correlation, using that to argue back to an earlier correlation, which is weaker than the collapse of the wave packet, and then saying, okay, this justifies us therefore using this earlier correlation, weaker than the collapse of the wave packet, to argue forward then and explain causally the existence of this correlation here. Now for those of you who still have a residual worry about this being a rather peculiar explanation pattern, what we've done is in fact said that the explanands, explanandung, justifies the explanands and we've used the thing requiring to be explained to justify the thing that's doing explaining and we've then concluded, sorry not therefore, we've then completed the circle by using the explanands to causally Explain the explanatory. For those of you who think there's a vicious circularity involved here, I refer you to Scriven articles in Minnesota 3, and he makes people very, very happy. I hope that indeed this sort of apparent circularity explanation is not circularity at all, and actually when you think about it, of course it isn't. Because here we have justification, here we have explanation, and it's only if you have a model of explanation, which is a crudely impelian one, where explanation always has to be predictive and hence, in a sense, just contradictory, it's only if you have that idea of explanation that you would be worried by this sort of circularity. So I don't think one has to get upset about this model explanation. It's not as elegant as the collapse of the weight of that explanation, which gives a lovely explanation of the Cartwright correlation without the need to introduce these sorts of... There is, of course, a cost to pay for this very neat explanation. The cost is that it is actually inconsistent with the laws of quantum mechanics. So I recommend to you to use this weaker explanation and get rid of the inconsistencies involved perhaps. Well, that's all I want to say.

5:00 I've shown that the collapse of the wave packet isn't needed in quantum mechanics for explaining counter-correlations, I could have extended this argument to other areas, scattering theory, and so on, and show that in each of those cases you don't need the collapse of the wave packet. It's always some sort of an over-strong excuse for a much weaker set of correlations which will do the same job. So I've shown that, it's not needed in this particular case, and I'm appealing to you to say... We could extend this to other areas where the Collapse of the Wave Packet is used, and I've also demonstrated in the first part of the talk that the Collapse of the Wave Packet is actually inconsistently common, and these two together, I'm claiming, give good reasons for protecting the Collapse of the Wave Packet, and of course also to avoid all the nastiness that the Carpire keeps on realism. Thank you very much. Now we have a quick stage hammer. It's only just that, in order to stop the discussion, the people standing are always against this mode of reasoning. Although it looks, you know, lots of realism and all that, I would like to hear how you would take it, but it is a kind of thread of argument running in the back of your head, which other people are going to cry. So let me just remind you what the standard objections are for this type of proof. But the paper has come in two parts. The first part was a little bit lost over there. What you presented when you come to the Stern-Gerlach measurement has somehow been completed when you've correlated the spin components. With the actual positions and now we have a macroscopic, well now I think the play on the word macroscopic is due to the detection of the beam in a large number, but when you talk about macroscopic you normally read some large 20 minute apparatus displaying the thing and certainly that still means that the electron is wrong and you can't do this. So that's your meeting with these little micro-entities. And what really happens is a measurement chain. First of all, you correlate the Tomsberg spins with the axis of Tomsberg's momentum, which is really what happened. And then, as we come out of the magnet, that's Tomsberg's kicks in momentum, and Tomsberg introduces Tomsberg's expensive positions.

7:30 That's really already another sketch of the measurement chain. But then you really complete the measurement. And there you get all kinds of successive steps. You don't need to maintain one thing in correlation with the other, ultimately you get a whole black spot or something. And that really matters on the science. But I want some people to know that the way you look at what Henry said about the way you can distinguish the four states, he said, well, there are observables that are more sensitive and can steer these two. But these observables have a very special character. There have to be correlations between them. So then people would say, well, on the platform, what about the second part of it? So people would say, well, don't you have a measurement chain, which I've heard people say, that means you're taking it from one side, to the other side, to the other side, to the other side, to the other side, to the other side, to the other side, to the other side, to the other side, to the other side, to the other side, to the other side, to the other side, to the other side, to the other side. C-I-S-I-I, for example, can be related to I-more, Chi-more, O-more, O-more, O-more, O-more, O-more, O-more, O-more. It's not to do with correlation, it's to correlate something with the plane of the system, with the time on the side, with the next step, the motion of the chain, the next step, the next step, and in this case you have to have a full-fold correlation in order to demonstrate a sensible, so-called, sensible result. But if you just correlate three things, the thing won't be sensitive because the other terms will be killed by what the reality is, the next bit of the motion of the chain. And so people have said, well isn't that just explaining the infinity? Well, then surely he's coming back, preventing any extinction of the electric mixer. Well, now this is a kind of limiting officer of all the familiar. If you give me a different number of steps in the measurement check, a fixed number, or you count it with n,

10:00 that's how you're going to make it. Even if you have a fixed number of steps in the measurement check, then it is always true that I can choose an n-fold correlation measurement which will distinguish the mixture. But on the other hand, it's also true that... If you give me any measurement of perceived like language, if you give me another one, what the correlation is going to be, I can always choose an N so large that that particular correlation will fail to make a distinction. So you have a sort of rather delicate situation here. Some people who claim the measurement is a little bit of a problem need to go to this leading neighbor and in some formal sense you can call for them and show that you get, well, non-unitary, if you like, head of work on this sort of program. But of course, one would wonder exactly what the physical significance of any A-character, any A-finite, then for any P-scale, as I said, you always find that there's really multiple correlations in certain states. Well now, some people then fall back on a kind of pragmatic argument and say, well look, suppose, in the typical theory of the web, a spot develops on a holographic plane, suppose, for example, there are 10 million states in a particular scale. They say, well, how do we do a 10 million-fold correlation experiment? I don't think that's beyond any possible practical. If you start getting up to a number, it's totally impossible. But people say, well, in practice, it's totally impossible to do this big correlation state with this source. It's the one that really is a pure state, and that, for all practical purposes, is not the same. The response to that is... So that's my first comment. It's just been a measurement schema which just has two steps in it. This has a really, you know, I think, attention to it. All of these have lots of steps in the measurement chain, and it's a very important point that you do need, for any steps in the measurement chain, you need an n-fold correlation to have a sensitivity to all of this.

12:30 Would you? I mean, there are a tap or a second. I mean, I don't want to say that solves the thing. I mean, all the time, all of you are trying to solve it in that direction. Does that mean that there is no measurement actually, you know, described where people could say this measurement is inconsistent with the assumption that there is a mixture, because it depends on the way of explaining the measurement? Well, they've both correlated, but I'm excited to know if James will actually tell you that this is not correct from the point of view of physical physics, which is described in his lecture, but it must still be described in his lecture. So this will let me get to it. But let me get to the infinity, not the subtlety, but what happened exactly. Now this is the simple, but careful approach to the problem, the language problem, and the style of the book, which is that we're all going to take on a team. For the time being, everyone has to call back on some sort of fact that they can say, well, it may be bigger than 10,000, or it may be smaller than 10,000, or it may be smaller than 10,000. So what worries me about this one? I mean, I take the point completely that what I've done there is, in a sense, simplified the measurement process by assuming that already in the macroscopic deflection of the silver ions we have something which is sufficient to make the measurement, and of course that's an oversimplification, but then again, any model which anybody would put forward in quantum mechanics is going to be an oversimplification of the measurement process, and it worries me that when people... Thank you for your attention. Cartwright correlation, which does not use the collapse of... No, no, come on. That was my comment on the first question. I know, but don't demolish the sense part of it. No, it's all about the different words. Small is, maybe underlined, is that it really, I think, forgets all the rest of the algebra. And if you just object to the word small is, it will only object to the crucial part of the proof.

15:00 But the possible relevance is in the kind of own-dominant practice which is related to what I said about this correlation thing, because when you just have a correlated state like this, just two steps to the correlation, then it's well known that if you make any measurement simply on this system, called in cubes, and some other called in fever, and size, the size of a cube, the velocity of it, the detection. But it's well-known that this type of entangled state, that if you restrict yourself to the measurements of the cube, expressed in the cube's course while on that joint space, that no measurement of that form can be sensitive to the distribution of the thought that it's a mixture. In order to make the distinction, you've got to do a correlation. See, that's what I said about the integral of correlation. And so, in that sense, if you restrict yourself just to measuring the cube, the thing behaves like a mixture. And through them, from a mixture, for this reason that, you see, this is what we'd actually talk about, what it said to you, that if we kind of look at the smallest room of space that you act on, you're kind of just acting on the space in the first system. And if it looks like a mixture in respect to that action, then it's really got to be valued, this is what was actually said. But now what people say, if that was true, I will prove another contradiction. Well, this is what Henry knows perfectly well what I'm going to say now. If in fact the system does have determinants at it, then what can the state's incompetence system be? And one seems almost driven to the fact that the state's incompetence system is like this. It's one is a half. And of course that is definitely not equal to the state's... In other words, for this axiom, you can, by assuming the inevitable logic, reduce the state of the composite system, which is definitely not the state from which you start.

17:30 Now, Henry knows I'm going to say that, I suspect. And of course, this destroys the whole chunk that I have now, if I were that to observe it. You know, I've demonstrated the complication of one of the assumptions, so, anyway. I agree, and there seem to me to be two lines of reply. One is to get rid of the I don't think so. I think all I need to do is reject some implicit assumptions which go behind making the step to this. Because that's, in a sense, a formal reply, I think what I have to do is, in a sense, motivate, give a physical reason for why we should take this acting seriously. And then give the formal reply. Because I think if I just give the formal reply, then the usual... And finally, there's a lot of different spots I get from people that, well, yes, look, perhaps formally that doesn't follow, but my gosh, it's awfully plausible to think that if you've got, you know, you get your sort of argument. Cliff Hook makes this line, he calls my approach a super cool approach, which is meant to indicate that I just, you know, formally, okay, Cliff, you can get out of this problem formally, but, you know, you're giving terrible violence to our intuition. What seems to count against the answer is I think indeed the very language in terms of which we have been brought up to think about mixtures, that is to say, Hispania's famous distinction between proper mixtures and improper mixtures. Now if somebody tells you that X is a proper mixture and that something else is an improper mixture, well there's something fairly pejorative which you're led to think about the improper one and you think, oh my god, well you know, I can't really rely too much on that. And what I, in fact, want to suggest is that we should reverse the Espana notation. We should refer to mixtures which are, you see, what's going to work here is the notorious ignorance interpretation of mixtures. If we have these entangled states, entangled states like so, then it's indeed the case if we have a Combined system, system 1, system 2, in an entangled state like this, then indeed, as Michael points out, or this is just the von Neumann theorem, then we get each of the subsystems in a mixed state, p by i.

20:00 And this one here is in a mixed state, sigma c i squared p psi. Now you see, what Desparmia says is, he said, look, these can't be proper mixtures here, because if this was a proper mixture... Then surely this original thing here, the larger system, it too would have to be a mixture. So this therefore must be an improper mixture. So, just by definition and a very weak sort of argument, I mean, why on earth, because this is a mixture, should this be a mixture? I'll explain why people think that in a moment and try and counter that, but I mean, that's what Despanier is appealing to. This is a mixture, well surely from, you only get a mixture, you can only have uncertainty in a subsystem. Notice the word uncertainty lies at work here. If you're up for an uncertain state in this system, because you've got probabilities, and probabilities mean uncertainty, if you've got uncertainty here, well then surely you must have uncertainty in the... And so on and on and on and on and on and on and on... We don't know what state the system is in, but there's a probability P1 that it's in this state, a probability P2 that it's in this state, and so on and so on and so on. So we therefore say the mixture is like this, but really it's in a pure state, we just don't know which one. He wants to reserve the term proper mixture for that. Now if you say that's your proper mixture, then indeed, when you go to the super system, it is indeed the case that you can't lose uncertainty by just going up a level. Now what I'm suggesting is that we ignore totally that particular interpretation of probabilities in quantum mechanics. We get rid of the idea that probability is just a measure of ignorance. We take the idea seriously that probabilities are propensities, objective, physical features of systems, and have nothing to do with uncertainty. Now if that's the case... Then indeed, we lose entirely the argument which makes us feel this is somehow inconsistent with this, and this is just the state description of the system, and this is just the state description of the system, and there's no question of talking about information or uncertainties at all, these propensities. So, I think that is what's behind the desk money I'm applying, it's behind Michael's response to this.

22:30 So that's going on in the ideology of the argument here, but the formal point that Michael was making was, how can we resist the move from this mixture here, this mixture here, to saying therefore, really what we should have, if there's a probability mod c i squared, it's just an s1, let's say it's s1, and this is s2. If we say there's a probability mod c1 squared we have phi1, mod c2 squared phi2, and similarly mod c1 squared psi1 and so on, if we have it, how on earth can we resist the conclusion, if we assume there's a correlation between the phi i's and the psi i's, how can on earth can we resist the conclusion that we've got the real state? It's really this, because if there's a probability mod c1 squared that the state is phi i, and there's a correlation between phi i and psi, then surely we should have a probability mod c1 squared that there's p phi i cross psi, and that contradicts this. And that's the form of contradiction that Michael was alluding to. We've got two forms, basically. That's right. Now, that's what I've got to counter. Now, I think that the way one counters it is as follows. One says, well, look, my challenge is to spell out the logic which gets you from here to here. Now, as far as I can see, the usual way that people make the argument is to say, look, If we have it in this mixed state, what that means is, and again you can see the ignorance interpretation of the mixture, that means that there's a probability, mod ci squared, that S1 is in the pure state for all i. So the mixture means that there's really a pure state with this probability. Similarly here, there is a probability, mod ci squared, that S2 is i. Now is indeed a law of quantum mechanics that S1 is in the pure state phi and S2 is in the state psi and S1 plus S2 has to be in this state, in the cross product state. So it would indeed seem as if I'm driven to say therefore the combined system would have to be some sort of combination of these phi i cross psi i.

25:00 But of course where I reject that argument is indeed in this step from here. So here, I want to say, look, this is Despagnat telling us that mixtures are always excuses for somehow uncertain versions of pure states, but there's always really a pure state. We just assign probabilities to it. That's what this by now calls the problem mixture. And if we do indeed make that move, then I agree totally with what Michael says. You can see what you're asking. The axiom is really the axiom. It's totally like what you lied or interpreted. That's what he said. I've made a varying point about it. I've talked about determinate values. I've got to deny one version of the eigenvalue eigenvector connection and that seems to be a good thing to deny because what I have to deny is to say this move Q has a determinant value Q sub i therefore let's say Q for s All of these terms can be used to determine the value of q sub i, therefore s is in a pure state. Now that's the inference that I have to deny. Yes, this is a version of the van Fraassen effect. Now that is indeed exactly what I'm denying. Now somebody can say, oh gosh, well that's terribly implausible. And I say, not at all. It comes as a direct consequence of the axioms that I've put forward here. And I say, but look, that's again one of the implausible things to deny. And I say, look, but look at the results that come out the other end. What it means is that we can get rid of the collapse of the wave packet. It is after all a reasonably natural axiom. And also, I claim, although I haven't done today, you can solve the Einstein-Kowalski-Rosen parallels, Schrodinger's cat, and so on. So, this is indeed the thing, what I have to deny, and what I'm claiming is that it's a very small price to pay. What you would have to do is give an independent, terribly strong argument for retaining this. And I'm not denying this in the case where there's probability one. If there's probability one that Q has value, Q . Then, yes, I agree that it's in an eigenvector. So I'm just denying it in that very special case here. Yes, that's right. In fact, the real problem with this, and Michael was very kind not to bring it up, was the fact that, and this is what I think upsets physicists very strongly,

27:30 is that this particular axiom here, in the special case we have a system which is an identity operator, Let's say that we have a system in which the density operator, Wst, is equal to the identity operator, let's suppose it's a finite dimensional Hilbert space, then we know that that can be expanded as, for any more than normal base set, Fi, this identity operator can be written here. If you look at this axiom here, what this means is that in this special case where you have a density operator which is an identity operator, every single physical quantity has a determinant value for that system. But of course I'm not saying that that is generally the case. So this is not a hidden variables theory. A hidden variables theory says always all physical quantities have eternal values. I'm saying that in this special case they do, and they do it for a very good reason, because of this axiom here. But I of course have the same problems that hidden variables theorists have. I have to face Gleason's theorem, I have to face Bell's inequality, I have to face the Redhead-Hayward result, and the whole program then, in my view anyway... It goes on how I get, how I cope with those problems. As I say, I have all the problems I have additional advantages which they don't have. In particular, I still retain the notion of indeterminacy. I'm quite happy that properties can have indeterminate values, and that enables me, of course, to use the orthodox Bohr explanation of the double slit experiment, which I always feel is the big disadvantage of invariables to people when they try and explain interference effects. So I can explain interference effects using indeterminacy, but I have the difficulty that invariables to people have because of this consequence here, but as I say, I think those problems can be solved. I'm sorry, I, I, I, I, I, I, I, I, I, I, I, I, I, I, I, I, I, I, So, in other words, I use the hidden variables response, essentially, to the R system, but then I, of course, inherit all the problems that the hidden variables people have, in particular Bell's inequality, and threats of non-locality.

30:00 But I think they can be overcome. The problem of non-locality, I think, can be overcome along the line that both Hellman and Redhead have put forward, that is to say, you give up. Determinism, not in the sense of classical determinism, you give up the principle of counterfactual definiteness, what's that? Well, it's the principle of counterfactual definiteness, and I think you can get out of the locality difficulties that way, you can avoid Bell's inequality, so it's then a whole program which devolves from taking this line. But certainly the SBPR are obviously solved trivially in the way that Einstein would have wanted to solve it, that is to say the correlations are there all along. That person picking up this eigenvalue or eigenvector in some cases, that Gleason's theorem isn't effective because Gleason's theorem is about some faces of Hilbert space and here only Conner McCallum is talking about some faces of Hilbert space. That's right. The Gleason's theorem can be similarly avoided. It's not a problem. But essentially what I do for the leasing theorem thing is to de-optimize. I mean in that sense what I'm doing here is a version of what I think Van Presten calls the anti-Copenhagen variant of the possible range of interpretations of quantum theory. It's a special case of the anti-Copenhagen variant. Although I don't like that term because I think Bohr, I mean what distinguishes it is from given variables is that I want to retain the notion, Bohr's notion, the Copenhagen notion of indeterminacy. I mean that to me is one of the great central insights of quantum mechanics, that you have ontologically an indeterminacy in nature. It's not just an uncertainty, but it's an undestimmtheit rather than the undeneuigkeit. Undestimmtheit meaning indeterminacy rather than the uncertainty, undeneuigkeit. And I think Bohr was absolutely right on that, and I think there are certain phenomena in quantum mechanics which require you to speak out of this indeterminacy. So I don't regard this as Andy Koppenhaugen in that sense. It's Andy Koppenhaugen only as a state-of-the-art term, let's just say the term that Van Thressen introduced.