Quantum Mechanics of This Specific Universe / Extracting Predictions from the Wave Function

0:00 Thank you for your attention. But we have till one for questions at the end of the time, Ted. Did you identify as crucial for the whole picture certain properties of rho naught when you said it was wound up? Yes, wound up with respect to certain variables, because the wound up mess is not possible to describe otherwise. All rho's are, well, no, I'm sorry, there is a difference. A rho can be pure or impure. But apart from that, they say they're all pure. All pure rows are equivalent, except if you then specify some set of variables with respect to which their entropy is coarse-grained. Then you begin to distinguish them. Well, I'm not in that field to answer that question, but as I understand it, there are two schools. One is that rho naught, for the universe, not the sub-universe, for the sub-universe it's presumably a result. For the entire universe, there may be a simple rho naught. Elegant, no boundary, boundary condition. The same kind of elegance, self-consistency, simplicity, whatever it is, mysterious simplicity, as, say, superstring theory for H, which obeys the bootstrap. Maybe there is a remarkably special condition. The other possibility is that a huge generic class, they're filtered out by the inflation and reheating of the sub-universe, the bubble,

2:30 and that really it's the wound-up-ness of that bubble that matters, and it's a gigantic set of Ronauts who have all done the job. I wouldn't know how to enter into that. If I did, I would just duck. In the latter case, though, you wouldn't, if the whole universe, then at the time of re-collapse, we don't have the same... Yeah, but there's no reason to believe it, unfortunately, if it is certainly very close to the boundary line. No, but what I want to emphasize is that the most usual, the usual guess now is that it is just on the closed side. A cosmological constant of negligible size might be enough then to avert the re-collapse, I am told, by it. And therefore, we don't really know even if it is closed. But you're right. If it does re-collapse, then that makes sense. I have to assume that question. Could you envisage a Ronaut that, let me say it crudely, a superposition of observer tracks, sense of the era of time? I've been doing all this work and I've never told anybody about it. But there I told people, I had a lecture on it, and at the end I said one thing that's interesting is this, if it's really going off, it's giving us the hour of time, then in a universe that re-collapses, during the re-collapse will time go the other way? And I should have ducked if people started throwing things and so on and so on. Well, Stephen Hawking raised this same question some 20 years later, and he was shot down, for example, by Don Page. And it looks as if it's not true that the re-collapsing state, you would still have entropy. But in both phases, my question is, if the expansion and the re-collapse, can the expansion, for one, be a re-collapse for another set of branches? Can they both be in there in the same place?

5:00 Could you have a role broad enough to encompass? That's a very pertinent question. As long as they declear. Now, the reason I left them out is that Jim and I are afraid that the Hardwell-Hawking theory can actually go outside of the whole quantum mechanical framework that I've been describing, a framework where the sum over tag is e to the i-s. It's conceivable that the Hardwell-Hawking proposal has both e to the i-s and e to the minus i-s in the second-order Schrodinger equation, the second-order Schrodinger equation being in some manner identified with the Wheeler-DeWitt equation. Now, if that's true, then they have a responsibility to show, and I believe they do, that the e to the i s or the e to the minus i s is then preferentially selected by some early measurements, but that's a whole other story, because I was talking here about an e to the i s quantum mechanic, and I was not getting into these wider discussions. So you've raised actually two questions in one. It can be answered within the framework of regular quantum mechanics, or there's the question as to whether you have to go outside regular quantum mechanics. Yeah, I wanted to ask if either of you or Zurach have any comment on the work of David Albert about self-observing on quantum physics and the ability to simultaneously become a non-convenient observant, the baddest of non-convenients. Are you familiar at all with David Albert? I am vaguely familiar with him. I think one of the properties of a system that's acquiring information would have to be a property of being able to acquire information by itself. And I'm not sure, you know, whether this... First of all, one would have, as Mario indicated, a much better idea of what these ideas are and what sort of requirements they have to have.

7:30 I might get to talk later a little bit about it, with an assumption that high-good is equivalent to a three-month-and-a-half-month or a month-and-a-half-month good sentence, okay? Don't worry. But it's a big... Well, but you should build in behavior, co-evolution of it. It's very important. It's very important in the present intellectual climate. People always trying to think of everything in terms of information processing. It's extremely important to build in behavior because it's the external sign that some kind of complication really is going on. So it has to intervene in the outside world in order to change the variables on which it's computing the information. It's amazing how many people make models of complex adaptive systems in which the system is completely passive and does only information processing. When actually in any real situation there is always behavior or co-evolution. If you look at all of life, for example, considered as an ensemble, it interacts with the physical part of the biosphere. Oxygen, for example, is thought to be there because of life. The early oxygen escaped. ... so-called inclusive fitness, or whatever. But in fact, if you look at the whole equation and its result, there is not a meaningful, sensible-looking Lyapunov function that steadily increases and that corresponds to the sum of inclusive fitness or the sum of foraging success or the sum of whatever it is. And so you have to look at this equation lacking this Lyapunov function that makes sense and somehow see in the differential structure of the equation its partially frustrated attempt. To bring about the improvement of certain things. Which goes to dead ends, does not always proceed to equilibria. If there are equilibria, they're usually not sensible-looking equilibria that make sense in terms of inclusive whatever it is. So the definition of a complex adaptive system is still not given. And it's very difficult to get. But one should not make compromises, I believe, by leaving out the element of behavior or coevolution or interference.

10:00 You want to grasp the problem of free will on top of that. No, it may be that when we understand the complex adaptive systems better, understand what they are, what the definition is, for one thing, how they work, that then our subjective notion of free will may not seem so mysterious. Wheeler would call it teleology without teleology. Effective obtaining of teleology without building it in at the beginning. But they lift that in the 18th century. You want more than just a question of pseudo-theleology. But you're absolutely right. The thing to do is to see these equations, find the properties that they have, even though they don't have sensible looking . Entropy is in the same character. Entropy does not strictly increase either in any sensible equation. It's only in radical approximations that entropy steadily increases. In any real problem, entropy goes up and down and so on, and it has this to increase when you're far from equilibrium. Very strong tendency. And I think it's the same with these other problems. So it's again an abscissa voliapana function with the presence of the spirit of voliapana. I just wanted to make a quick comment now. In particular, because of the importance of this decoherence that both Wojtek and Murray have mentioned, and that was this model problem that we looked at, which again is a harmonic oscillator connected to a bunch of other oscillators. In this case, some free scalar field operating in one dimension. And you get the ordinary damping out of it, which depends, the fact that we get the damping rather than the anti-damping depends precisely on the fact that one chooses the initial state of the field rather than the final state of the field. Can you stand next to the screen, please? Sure. And as Wojtek mentioned, what you have to do is insert a cutoff, which in the problems that we've looked at, we've taken a cutoff that's about a thousand times larger than the frequency. And for the case in which the damping coefficient is about 0.1 of the frequency, so it's a Q of roughly 10, you get some rather astonishing results.

12:30 For example, if we take a squeezed state where the squeezing parameter is squeezed in the P direction by a factor of about 3, so this is about 8, actually the one we took was about 8 times as long as it is wide. This is the Wigner function, a sort of a plot, a contour plot of the absolute value of the Wigner function here. That same function, if I look at the density matrix in the Q representation or the P representation, I get things that look like this. If I now go just 10 to the minus 2 times over omega later, so this is sort of 10 to the minus 2 of the natural frequency of the system later, I get something that looks like this. It increases in the p-direction. The off-diagonal correlations, the diagonal and the q-representation, the off-diagonal correlations just drop dramatically even in that extremely short time period. The on-diagonal parts of the p-representation move out because you've effectively done a measurement on the q's which makes the p's uncertain. And the interesting thing to do is to compare that with what happens if you squeeze in the p-direction. So here we have the Wigner function again. It's squeezed in the, it's now squeezed in the q direction. So now the p density matrix has large off-diagonal terms. The q representation has small off-diagonal terms and it's small in that direction. If we now look at what happens, oops, which one? That same 10 to the minus 2 seconds later, nothing happens. So I think this is a dramatic illustration of how, you know, it's the Q representation that's important, and one gets very rapid decoherence if one has sort of coherence over appreciable distances in the Q representation, but one doesn't get that in the P representation at all. But wasn't that put in by a coupling? No, the coupling was very, I mean remember I took a coupling such that the damping term was 10 times as long as the natural period, so it's a Q of about 10. So the damping is actually a weak damping, the thing oscillates for a long time.

15:00 It's only over time that the basis is chosen by the coupling. Sure, the basis was controlled by the coupling, yes. So your statement is really that it is true. Just the same as his. I mean, it's the coupling that determines how the coupling to the environment determines which one of the various bases are picked out for rapid decoherence. And so the mystery is still the same as Carol had pointed out, namely why... And they're given to you by the equation, whatever your equations happen to be. This is an interesting case as well because here Q is not conserved by the Hamiltonian Neither is P. They're both on equal status with respect to the harmonic oscillator Hamiltonian. The only place they're coming in is with the interaction in the environment. And the other thing that's interesting here is exactly how rapidly everything happens. I mean, 10 to the minus 2 omega is a time scale that's sort of relevant to nothing. It seems, and yet, except for the cutoff, that's sort of that cutoff time scale, and yet you're getting this very rapid coherence on something that we would really regard as a quantum system. Remember, I've only squeezed it by a factor of about three, so the wave function looks really like a quantum wave function, as far as almost everything is concerned except the environment, which very rapidly squeezes it down. Thank you. It squeezes it between the two sides of it. Right. Okay, I'd like to make a kind of comment and pose a question to both speakers and to other people as well. The first comment is that I think both of these talks to me represent enormous progress in understanding the interpretation of ordinary quantum mechanics, and it's really very gratifying to hear them. I'm pushing everything back to the theory of the row of T naught, which we'd like, ultimately, to be able to understand, and I'd like to suggest... In this connection, if Carol won't mind, I'll use a comment that he made in a review of a book reporting on a similar meeting several years ago, in which foundational problems in quantum gravity were discussed, and his comment was that people start off, as Wojciech did, with the first thing we're going to discuss, the quantum mechanics of the universe, and then from that point on discuss the interpretation of ordinary quantum mechanics. And I'd like to suggest that when we...

17:30 I actually tried to understand the interpretation of the kind of state functions that come from quantum gravity. We have a situation which is qualitatively different than ordinary quantum mechanics. The Wheeler-DeWitt equation or the Hamiltonian constraint equation of quantum gravity is very different from the Schrodinger equation. It is second order rather than first order. It is real rather than essentially complex. We have a situation where we have no idea what time is, where we're very confused about what the inner product is or what the inner product might mean, and we're in a situation which is radically new and very different from the problem of the interpretation of quantum mechanics in the Schrodinger equation, and it seems to me that there's, I detect a sort of feeling that, well, if we figure out how to interpret quantum mechanics, it's only a small step to apply this. I certainly didn't say that. I was not speaking on that other subject. My colleague is going to speak on it, and he knows about it. I wasn't speaking about it because I don't know anything about it, but the fact is that the universe as we know it is descended, if the new inflation is correct, it's descended from a reheating bubble after inflation, which already possesses most of the features that we need for this purpose. So that it's very unlikely that we need, for most of the stuff we're talking about, to appeal to the antecedent history of the universe, interesting as important and fundamental as it is. Because most of it has probably been strained out. Only a wide, any of a wide class of initial conditions for the whole universe would probably have led to this situation with the, after the inflation. That's what we don't know. Well, it might have, anyway. As I said, I don't want to get into it. We don't know that. Could be either way. Could be a wide class or it could be that you especially need a very simple row of t naught to get there. But that's why I mentioned both the sub-universe and the universe. For practical purposes, it's the sub-universe that we're really dealing with the heritage of the sub-universe in most practical cases.

20:00 And yet, it is the heritage of the whole universe that is fundamental and interesting. And the relation between those two is still somewhat unclear. I think if I could just finish my comment, I think that's a certain hypothesis. Those of us who work on quantum gravity are faced with the problem of giving an interpretation to the results of our work. And I'd like to really end this comment by mentioning three criteria that I think in any attempt to interpret... There is no such thing. Well, if there is no such theory... Everybody knows there's no quantum gravity, there's only super string theory. The only theory that's ever been written down that reconciles quantum field theory with Einstein's gravity is super string theory. Well, we'll perhaps try to convince you differently of that tomorrow, but... You can try. Yeah, okay. The second criteria is that the interpretational method should apply to all solutions. The third criteria is that if an interpretation ever uses the word probability, or something which is defined to be a probability, all those probabilities must add up to one. And I'd like to challenge people who talk about quantum mechanics or interpretation of wave functions of the universe to give us an interpretation that satisfies these three criteria. We're faced with a social situation in which the superstring theorists have until this moment, I think it's now changing right this month, until now they've shown an extraordinary unwillingness to deal with all these questions of principle about cohomology and how superstring cohomology looks. Whereas the people who deal in so-called quantum gravity, which doesn't exist, have been unwilling to learn the only theory that we have at the moment for attempting to cope with it, namely super stream theory.

22:30 They're very concerned, properly so, with these fundamental cosmological questions, but they haven't bothered to learn the theory. The people who work on the theory are uninterested in quantum cosmology. I find this situation insane, and have said so for a long time, but it's changing now, fortunately. And I think it will be the union fusion of the two fields, if one can overcome these sociological obstacles, will be very fruitful. Wouldn't you agree that there's some problems that are probably common to both attempts to make some sense of quantum general relativity or quantum gravity and string theory? Since quantum general relativity doesn't exist, I don't think it's essential. No, but string theory is supposed to contain it, contain gravity. Oh, yes, but as a divergent approximation. If you try to chop all of these... Well, that's perturbation theory. I mean, I don't think that's an answer to the question at all. When I arrived at the Institute for Advanced Study in January 1951, the first thing I heard was that Ning Hu had shown that the pseudo-vector meson theory, which is highly divergent in perturbation theory, was in fact convergent if only you used non-perturbative methods. And then 20 years later, Abdus Salaam took me to lunch and explained to me at great length how he had proved that quantum gravity was fully convergent if only you used his patented non-perturbative methods and so on. I'm still waiting. What would you like to comment on David Gross' recent paper about perturbation theory and string theory not converging or being correlable in any sense? I don't, didn't read it. Can I ask you sort of the inverse of this question? You presented a very beautiful and impressive and coherent quantum story. But aside from this sort of abstract ordering parameter, which you call a time, how does the space-time structure come into it? Does it have to be inserted by hand, or do you have some way of... Why does it seem so important that everything takes place in space and time? Why is there a space-time structure? Is this adventitious? And you have to appeal to string theory, which is... If string theory is the correct theory of the entire world, which it may well be, it or some successor, which has some similar properties to it, if string theory is correct... Then, it indeed has the responsibility for explaining, either by dynamical or environmental means, in other words, with either by itself or with rho of t dot in addition or with alphas in addition, how we have the space-time structure that we have.

25:00 And I understand that Gary will speak about something like that, but that's a very big question. You have to answer it carefully within whatever is the correct theory. So you say it has something to do with the Hamiltonian. It happens to depend on some variables. Are you going to deduce those variables later on? Well, the superstring theorists are debating that. They're not sure whether to use the two-dimensional structure of superstring theory as the really fundamental structure and to have space-time fall into play somehow, or to use a ten... A dimensional or other funny dimensional structure to describe the theory and then to have some of those dimensions put themselves out of the way with an approximation and so on. There are various methods. Nobody knows what is the most convincing way to solve the equation. But anyway, it's an extra ingredient that has been put in by hand. It doesn't flow out of your... I'm just asking. I'm not based on... In fact, I was starting at an era when all these questions were largely over deliberately because I wasn't trying to talk about that. It's obviously very important. I want people to work on it. I think it's tremendously exciting. It's just a pity that most of the people who have worked on it today have been blind... up to today have been blind in one eye or the other. If we just begin at the era at which all these questions have been settled in some sense, and therefore we do have a classical space-time, and so we know what space and time is, and now if you take your viewpoint and if we were to look back at the Copenhagen point of view, I mean, certainly this role of rho naught was completely ignored. That's the main point. But then at once you had a transparency in which, for example, you said, but also you want to emphasize that there is no need really to separate. The classical world from the quantum world or this measurement being an object, you know, some process like that. On the other hand, you had these two things in the whole discussion. One was this IGS and IGUS. And I thought that these were just different worlds, different worlds. In other words, if you were able to explain what Bohr or what Copenhagen school was trying to say in your terms, then I thought that you were going to say that, well, it is when aegis intervenes, as you said, that it normalizes the probabilities.

27:30 That isn't actually what they said. That would be a fair thing to say. You can, if you want, say that. But then, if I do say that, then I'm sort of... That's right. And I would like to encourage a tremendous amount of research on complex adaptive systems so that we understand them better, because if that's where we're hung up... And let's understand them. It's a scientific subject. It is an interdisciplinary scientific subject. It embraces economics, anthropology, linguistics, psychology, neurophysiology, computer science, physics, chemistry, and so on. All of biology. It's a very interesting subject and we should get started on it. I don't think that when we're finished with all of that that we will find that we have to introduce some special set of laws. I consider that extremely unlikely. We'll simply find that with H and rho of t naught and the formula for probability in quantum mechanics that there are certain systems that behave that way. So, I just want to, one last, you know, in the same lines. In this era that you work on, which is that the, there is already a classical space-time kind of thing, Roger Penrose also thought about These measurement questions, perhaps in the same era, and then came up with a proposal, which might be, which is quite different from sort of the U.S., but... Well, he doesn't believe quantum mechanics. He can't face it. No, but could... He's a distinguished predecessor in Einstein who couldn't face it either. He made him queasy. No, no, but... Presumably makes Roger queasy. No, I don't think so. I think what you call I guess, and this really is a question, could... He would like to propose something else, I guess. I want to say if you want to have any comments on that. Gravity? Well, the statement is that if in fact we are working in this era in which we have a classical background space-time, then in some sense the gravitational field is objective by assumption. It's there. It's not the position of something or something. More than the other components of the super-strain field? Well, I don't know. What's so special about it? We just agreed that we are working in this domain in which we already have. The classical gravitation field, right at the spacetime. The space, I mean, the answer to John's question, I thought you said. I know, but you're now going back to consider the fundamental issues. No, I'm not. If you're going to start considering the fundamental issues.

30:00 I'm not. I'm at this level. I'm at the same, I'm asking the question at the same level that, as you talk. Oh, I see. Okay. Namely, that the, well, take the universe as it is around, and let us try to talk about measurement theory or quantum mechanics in the environment. And then the question that his proposal was that, well, if in fact a phenomenon occurred in which the gravitational field changed by some well-defined amount, then a measurement took place. In other words, it is at that time the probabilities are renormalized anyway. And so... I don't understand. Because the Roger, I believe, wants...doesn't believe quantum mechanics. He wants to change it to something else. And then if that's something else, the gravitational field would have some magical properties. What we can say, if you want to ask about the role of gravity, gravity is coupled to energy density, basically. Energy density is one of these very quantities we were talking about. As soon as you get to energy density or one of these other NAIs integrated over a suitable volume, coarse grain, you get to the measurement situation. That happens anywhere, whether it's playing quantum mechanics, playing gravity theory. Late Euro and space-time is defined and so on. And no problem. If Roger wants gravity now to be endowed with some magical property of changing quantum mechanics into something different, that's a whole other story. But that is at some other level. That is at the level which is not covered in your talk. That is at the level of, you know, these initial conditions and what happens before space-time. But everybody would agree that without an igus, that you have a measurement situation when you couple to a solar volume of energy density. That's one of those variables that behave in this nice way in the universe that we're dealing with. Right, but he's proposing an igus, which is supposed to be the direction of the field. It wouldn't be an igus, it would just be an igs. Maybe there's no difference. Maybe there's no difference. I'm not persuaded that there is a line between them. But you are saying that that is just igs. I'm not sure whether there's a line between them or not. It looks that way. We've got to continue this. The function of the generalizing in classes of sigma and a space of solution of the entire set of constraints is defined, can be defined in class of form and contains the ordinary class of sigma.

32:30 Now I want to stress this, the new thing here, that these results are without any additional input besides generativity and quantum mechanics. There is a great number of open problems, and I can mention two of them, is that there are solutions besides this. One that I would like to mention is the following.