The quantum theory of measurement; subsequent discussion (contd.)

0:00 Yosen Tsai, already referred to, argued that the scattering by the planet of low-density material, even just the three-degree photons, Decoheres the planet. In other words, the x and x prime on the two sides of the density matrix are squeezed together with a huge coefficient just by the encountering of those little bits of fluctuation left over from the early universe, let alone all the dust and all the space launch debris and all the other things that the planet may encounter in the way. So the squeezing together of the trajectories on the two sides of the density matrix occurs through this effect. All of this, of course, made possible by the density matrix of the universe. The initial density matrix of the universe is what makes that possible. This is what apparently is called environment in the jargon of the subject. For me that means something different. A tropical butterfly. The orbit of the planet is predictable to high accuracy. Now that depends on something else. That depends on the fact that on each side of the density matrix one receives contributions principally from trajectories near the classical one. So that X and its conjugate variable are forming a little cells in XP space which propagate almost classically and on each side of the density matrix. So you have these two things. Quasi-classical behavior involves the concentration of the trajectories near the classical one on the two sides of rho and the squeezing of them by the encounters with all this space junk on the two sides of the density matrix. Third thing is that the trajectory is not much affected by these quantum fluctuations. The planet is meeting all these little photons and things left over from the early universe and a lot of other junk, and it keeps plowing away through space, very little effect. If it's a itself a piece of space debris, then the friction may actually amount to something after a while, and it may fall down on us the way that the nuclear reactor is going through. But, a planet that's got enough inertia is going to keep going without very little effect of that. However, sometimes it happens that a quantum fluctuation, a quantum event if you like, is amplified to the extent where it can modify significantly the behavior of one of these quasi-classical operators. And when that happens...

2:30 Then the rule that on one side of the density matrix or the other we are sticking to a classic given classical trajectory with very little contribution outside is modified and the trajectory splits or fans out depending on whether we're talking about a discrete or a or a continuous variable in the quantum event that's being measured. That's what a measurement is. In other words, the measurement situation occurs when the quantum event is amplified to the point where it significantly affects a quasi-classical variable and causes its trajectory on one side or on the other to branch or fan as a result of this interaction with the quantum system. But the quasi-classical behavior of the two sides of the density matrix remains. They are still squeezed by this environmental effect persisting from the density matrix of the early universe. That quasi-classical behavior is still true, and that's what gives the decoherence. So the decoherence must still obtain if we're to have a valid measurement. Now we're going to answer later what kinds of operators have these properties of habitual decoherence, persistence in the presence of the low-level quantum fluctuations that cause the decoherence, and possible responsiveness to certain amplified quantum events. I gather that these variables that like to do that are ones that then would be selected for this bird dog basis or whatever it was called. Was that the name? Oh, a particular kind, I'm sorry. Was it shorthair? Shorthair, huh? Setter variables, that's right. Setter variables, okay. Since it restores the classical rules for joint probabilities, allows the information from the valid measurements to be stored in commuting variables or approximately commuting variables that persist.

5:00 Now that's what was meant in the old quantum mechanics books. We are now interpreting in sensible ways all these crazy things they wrote in the old quantum mechanics books. They now make sense if we say them right. That's what they meant by the conversion of Q numbers to C numbers in a measurement. They meant that the information from a valid measurement is stored in things that commute to a high axis. Now, we have a textbook example of one of these fishy things where the universe is restricted to one or two things, and we have these measurements that allow the variable to continue as it was. What are they called? Non-demolition measurements? I have to learn the jargon of this peculiar tribe. Anyway, you have a psi equals little a psi, and then you measure another thing, b phi equals little b phi. And you have the initial state, and each one has an apparatus associated with it, Y recording A and Z recording B, then operator language in the following way, that for present data at present time t, we can have a lot of projection operators onto the left-hand side of the density matrix, all at time t. Which gives the same result as projecting onto the density matrix with p1 alpha1 back at time t1, p2 alpha2 back at time t2, and so on, for all of the measurements that have been made, they're all now stored in these q's at present time, and the q's commute, even though the p's don't. The projection of these onto rho is the same as the projection of these onto rho. When that's true, it's then trivial to show that when we take this trace, It's got to have complete decoherence. So in other words, the complete decoherence of these P's is absolutely necessary if we're going to be able to store the information than in commuting variables, commuting projections, Q. So the two ideas are related to each other, the notion of complete decoherence of the sequence and the notion of being able to store the information after slots. When it's an igus that's doing it, we call them memory slots.

7:30 But of course, these are not restricted to anything as fancy as an igus. The piece of mica has its variables, its commuting variables in which the information is. And we can say a word or two about history. It's most accurate to look at science from the point of view of an igus. If you say that the selected alternatives have been turned into a projection p alpha present data onto what is recorded now in the memory slots, that's really what an igus has to work with. At any given moment of time, it has to work with those. Now, you can improve this even more if you talk about sum over histories, but I won't do that. I'll just consider a single instance of time. Have the probability formula, the conditional probability formula, best expressed as p alpha n through alpha m plus one, these are the things that are yet to happen, and then alpha present data, the things that are stored today. This is the most honest point of view. This is the way we and all other iguses operate. All we have is our knowledge now. We have documents, we have memories, we have everything else. All of the history of the universe, cosmic, stellar, planetary, biological, human history, and so on, is constructed by an igus using rho of t naught, a primitive idea perhaps, but some idea of rho of t naught is essential in order to make any statements at all. And something about h. You've got to have some primitive notion about h in order to make any statements. It may be very primitive. And a primitive notion about the formula for quantum mechanical probability could be very primitive. But with those three things, then you can make predictions and you can also reconstruct probable histories. A detective, for example, examines present data, constructs plausible scenarios for the past, each of which makes predictions about further data that should exist. You know where to go and look for the bloody fingerprints according to that theory. You go look for them, and then you have additional evidence supporting that reconstruction of history. The historian operates the same way, the geologists and paleontologists, the cosmologists all operate in the same way. Crude approximations of the fundamental probability formula with h and rho of t0 are crudely approximated. And the row of t naught is such that it permits, in a great number of ways, a choice of p's from a fairly large set, such that you can get this good decoherence, this habitual decoherence, in terms of these variables.

10:00 And that's what permits, then, a meaningful discussion of alternative histories. The joint probabilities then involve a mixture of this classical behavior and then interaction, quasi-classical behavior, and then interaction with an amplified quantum event that fans out or splits the nearly classical trajectories and then more classical behavior and more fanning out and splitting and so on. In the case of Schrödinger's cat illustrates this. But it is not a special thing. The universe is sprinkled with Schrödinger cats. It's very important to realize. It's not an isolated silly little construct. The galaxy is a Schrodinger cat. The reheating bubble, the sub-universe is a Schrodinger cat, and so forth and so on. All of these things are cases where some great big thing has emerged a little. So we have the classical squeezing of the orbits on each side and the squeezing of the orbits on the two sides as well, together. Now, the classical phenomenon of chaos is often invoked. People say, when there is such a thing as chaos, which is classical indeterminacy, then how do you know you're talking about quantum fluctuations when you say that quantum events have led to all these big changes in the universe? The answer is that classical physics is false and quantum physics is true. And therefore, we don't have to compare with the classical world. All we have to do is look at what's happening in the real world. In the real world, chaos is just one more way for a little tiny quantum thing to be hugely amplified. Because what chaos gives in a nonlinear system with a strange attractor is an infinite dependence in the classical limit of the outcome on the initial conditions, which means that a little quantum change in the initial conditions can produce a huge effect. Nevertheless, people who have looked for chaos in quantum mechanics have looked for it in such funny ways that they haven't seen it, and this gave rise to an editorial in the LA Times, if you will. So, rho of t naught is essential. We said that before. It's essential for irreversibility, it's essential for the regularity of the environment. So let's talk about irreversibility just a little bit.

12:30 The thermodynamic arrow of time and the uniformity of direction for subsystems as they become approximately isolated. So we define entropy. If you define entropy accurately enough, as you all know, it's conserved. It isn't any use. So you have to coarse-grain it in order for it not to be conserved. And then you can show that it has a certain general statistical tendency to increase if, initially, it's very far from equilibrium. And I don't think I'm going to go through all that. It's just too much, and you all know it anyway. I've got some beautiful formulae and theorems, and I'm going to throw them all away, because there's too little time. You'll put them in your article. Yeah. The point is, though, that I do want to say this much formalism, because I think this formalism is useful. We've given a lot of examples of coarse graining, which I haven't let you in on. We want to ask this question. Given rho of t naught, are there operators that are natural foci of such special concern? I guess those are the things people were talking about during the previous hour and a half. Yield natural definitions of entropy as well as natural definitions of decoherence. And could it possibly be the same variables that habitually decohere and that yield a natural definition of entropy? Answer, yes. But we'll get to that in a moment. Next thing is, do we really want to separate all the variables of the world into two classes and integrate over one? Not always. Technically, that's not always possible. And so, what we do is introduce a formalism that doesn't require. We refer to the work of James as quoted by somebody or other. Who quotes him? Hobson. Oh, yes. That's the man who offered you one horse or no horse. And so we generalize his definition. He apparently included only the results of present data in his definition, if Mr. Hobson has it right. He ignored the density matrix of the universe. Our modification of Mr. James' work is to restore the universe to the work, so that we now deal with rho and then p present data on both sides divided by the normalized trace.

15:00 Otherwise it's the same. What you do then is you say that a rho twiddle is to be constructed, which is a coarse-grained density matrix. The coarse-grained density matrix agrees with the real Rho effective, which embodies the density matrix of the universe and all the stuff we know about this specific one. And the trace of Rho twiddle times anything we care about is equal to the trace of Rho effective times anything we care about. That way you can use operators that don't have to commute, they don't have to be one special set of variables, they can be any operator. And then you maximize the entropy, that's equivalent to taking the spore over a... But even though you haven't bothered to divide the variables into two orthogonal categories. So it's a very useful formal trick. S is then minus trace rho twiddle log rho twiddle. And it is the maximum possible S given that these conditions are obeyed. And of course trace rho twiddle has to be one. But this is the way trace rho effectively works. Using Lagrange multipliers, rho twiddle can then be constructed. It's here. And it has a coarse graining then. Which has the following beautiful properties. They are all the properties that you would demand at any coarse graining. Rho twiddle is now a function of rho effective, the function determined by the a's, by the things that are correctly reproduced. First of all, it takes a density matrix into a density matrix. Second, if you apply it twice, you get the same thing that you do by applying it once. So it is clearly a kind of coarse graining. And third, minus trace f of rho effective log f of rho effective, which is the new entropy, is the same as minus trace rho effective log f of rho effective, which allows us immediately to plug into a theorem that relates to inequality. So these three things are extremely, these three properties are very useful and they're all obeyed by this definition. And this just repeats what we said. By the way, we were able to do exactly the same thing before for decoherence, you know, we defined decoherence without having to divide the variable to the two kinds by utilizing the trace formula for the probability, which automatically takes the spore over everything that you don't care about. Anything that's not in the piece is automatically spurred over by the complete trace that's outside. So in both cases, we've gotten away from having to divide the variables into two categories. Now that's a formal.

17:30 Let me skip all these examples. Yes, yes, we're getting to that. What are natural AIs? What are natural AIs? That's the question. This was before, what are the naturally decohering variables? Now we want to know what are the natural AIs. Okay? The answer is the same. Let's look at thermodynamics. Suppose we care about one variable, A. Then rho twiddle is e to the minus F A times normalization. Then F is one over the temperature if A is the energy. And we can construct S. And then we perform the usual partition function, logarithm manipulation. U is the expected value of the energy. This rho measured is the same as rho effective. So U is the expected value of the energy. Then you learn by some manipulations that dU dS is kT, which is the fundamental principle of thermodynamics. Now the TESOL method of doing thermodynamics, as written down by Callum and published by Callum, You have the fundamental equation of thermodynamics, which is the extensive variable U, the expected value of the energy, expressed as a function of S, which we just defined, and then all other extensive variables that you care about, V, and then a lot of other extensive variables, magnetization and so on and so forth, whatever it is you have. Number of certain kind of molecules, number of defects. Whatever it is that you're concerned about. All things by the way that are not fluctuating today. So they're all extensive and they don't fluctuate too badly. You take the U as a function of all these things and then you define all the intensive variables as the partial derivatives of U with respect to the extensive variables keeping the other extensive variables constant. That gives you the whole of thermodynamics. Another example, by the way, which is interesting, is just to take a single set of projections. In which case, rho is just the sum over those projections, rho twiddle is just the sum over those projections of the probability of those projections. So the entropy then can be written simply as minus sum p beta log p beta plus the sum of p beta log trace p beta.

20:00 These are the dimensions of the subspace, the two terms there. If the subspaces all have the same dimension, then to within a constant, s is just minus some p beta log p beta. Again, a very familiar formula, and it was referred to by you. It goes back to Tolman, who in his book on statistical mechanics gave this as a quantum mechanical formula. It's very specialized if it's one case of the entropy. Now, I'm not going to belabor the business about the second law. It's easy to show. There is a certain tendency for S to increase when you start far from equilibrium, but it's very hard to show in detail that it really increases. In fact, I don't think anybody's ever really treated the problem correctly. The best information comes from the silly little example of Ehrenfest and Ehrenfest, the Ehren model. For that model, which you can solve, they show how, if you're initially far from equilibrium, there is a fantastic tendency to move toward equilibrium, and this describes it very well. That over long intervals, you spend most of your time near the maximum entry, which is the equilibrium value, the equally distributed probabilities is what we mean by equilibrium. The excursions from that get rarer and rarer and rarer as the coarse-grained entropy moves away from this equilibrium value. In other words, this is more information in the system. And that means that if you start out far away, then the chances are you're either moving back toward equilibrium And so there is this general tendency, when you're far away from equilibrium, for the thing to spring back. This winding up, therefore, of the situation with respect to a certain set of variables, when, with respect to those variables or operators, you're very far from equilibrium, that's the main feature that we experience with the universe. Rho of t naught is fantastically wound up with respect to a certain thing. And now, still, isolated parts of the universe are incredibly wound up in respect to those things. And it's not just the second law. It isn't just that there's a general tendency to increase. You can look around you and you see all these multiple occasions for huge increase in local entropy. All these occasions when things can jump ahead because the winding up is pervasive still in isolated systems after all this time. Just touch things and they move ahead in entropy. I won't bother to list all these.

22:30 Things that we say about it. But here's the theorem that I promised you. That s of a sum over alpha p alpha rho twiddle p alpha is always greater than s of rho twiddle except in trivial cases. And therefore a rho, a complete rho, can never undergo operator decoherence. But a rho twiddle, which doesn't obey the Schrodinger equation. So you can get operator decoherence only for a spool rho or a rho twiddle or something that's coarse-grained. There are other theorems that I might mention in passing, although they're not really relevant to this talk. If we talk now about the negative of the information held by an igus, that kind of entropy, then we want to talk about S of a chopped off, lopped off, row twiddle. Row twiddle lopped off by a particular p alpha that we measured, renormalized by the probability, so that it's restored to being a density measure. That S is invariably less than the S of the of the decoherent row twiddler. What if you do both of them? You go from row twiddle directly to this one. The answer is indeterminate. You have the two steps, one of them raises the entropy, the next one lowers the entropy, and the sum can go either way. Except that, if you take the average, then it goes only one way. If you sum over trace rho twiddle p alpha, which is the probability of getting the result alpha, and then you put in the entropy of the locked off configuration corresponding to the choice alpha, that average entropy averaged over the probability is invariably less than the original one. You always gain on the average. You always gain information by making that. So there was a difficult theorem to prove. It was conjectured and then several years later proved by somebody else. Okay, now we go back to the natural operator. We don't know much about them, Jim and I, but we thought a little bit about them, and we thought it was worth sharing the ideas with you. We have a set of candidates which seem to work for all of the various properties that one wants, more or less. And we haven't looked at all the examples and all the implications and the exact definition of the category and so on and so on.

25:00 So if you press us too closely, you will get... Professions of ignorance, lies, various other things, evasions, depending on exactly who's asking the question and who's answering. But roughly speaking, I think we probably are onto the right moralistic. And these things seem to work both as natural candidates for coarse-graining as well as natural candidates for habitual decoherence. And the way you get them is by looking at integrals over suitably small volumes, but not too small, of certain densities. And these densities are densities of conserved quantities or of approximately conserved quantities. The volumes are small enough, as in Landau's book where he defines entropy for a non-equilibrium system, they're small enough to have reached approximate internal equilibrium. But they're large enough so that they are not in equilibrium with one another and so that they change relatively slowly. Thank you for your attention. Say the density of a certain quantity a is n a, then we define a little n sub i a to be the integral over the volume v sub i of that density of a. And if we subdivide the volumes into a finer partition v i j, then we get n a i j, and these things have come into equilibrium with one another as far as the j index is concerned. And the n i j vary rapidly enough to do that. The bigger ones have not yet equilibrated with one another. Now in hydrodynamics, these variables are the central variables of the subject. So these are the variables of hydrodynamics, they're the variables of measurements, they're the variables of thermodynamics, they're the variables of classical physics, they are all the variables essentially by which we take hold of the big universe around us that's not quantum. In hydrodynamics, they point out that these very quantities, NAI, approximately obey a closed set of first-order differential equations like Navier-Stokes equations and things of that kind.

27:30 They're typically derived utilizing the internal equilibrium over this small volume. They're usually derived just for expected values of these operators. But in fact, it seems that in practice, in nature, given the nature of rho of t naught for the universe, These variables, these operators usually obey semi-classical, usually have semi-classical behavior as operators. It's not just the expected values, therefore, that obey such determinate equations, but to a good approximation, actually, the whole amplitude involving them, the succession of them, obeys semi-classical, has semi-classical behavior, quasi-classical behavior. In other words, they tend to exhibit the strong correlations that characterize this quasi-classical behavior for the contributing trajectory. Except, of course, for strong effects of occasional amplified quantum events, that's what makes them suitable for making measurements. Those are the things that make the trajectories themselves split or fan out once in a while, even though on the two sides of the density matrix they're still being squeezed by the environmental influence. Because the volumes are large enough so that these NAI are resistant to change, they hold up under these low-level fluctuations, the low-level fluctuations that cause them to decohere. Like, well, a big example was the mass of the planet Mars, of course, a huge thing that was very resistant, but it's also true for a little object that is highly resistant. Occasionally, they come into correspondence with particular quantum events undergoing the irreversible escalation to macroscopic status that characterizes a measurement situation. And then they are affected and they split or fan out. You can include approximate conservation laws here like atomic species, mass, number of crystal defects. In the case of the mica, it was detecting the fission tracks. Or you can have energy momentum, electric charge, and so on as in the usual equations, the things that are exactly conserved. Now a typical feature of a measurement situation. Remember, a measurement situation is what occurs if you have everything but the igus that's reducing the, that's renormalizing the probability of all the other features. In a natural measurement situation, and in any other measurement situation that we know of, there are many, many different patterns of the NAIs that are labeled one track or one measurement or one thing.

30:00 Redundant multiplication, redundant amplification of which Jurek spoke. And there's usually a huge entropy of redundant amplification within many, many, many copies of the information that one wants. The reason that happened is that the row of t0 was so wound up that the surviving, partially isolated parts of the sub-universe are still so wound up. It's very easy to get a huge amount of amplification, and you get then much more than you need simply to gain initial access to the NAI. You get a lot more. You get a huge amount of duplication in the photographic grain, in the bubble, in the cloud chamber or the bubble chamber. Whatever it is that you're dealing with, you get a huge amplification. It makes it very easy to read the result. Now notice that these same variables which we invoked on the basis of hydrodynamics are also the variables of thermodynamics. They are the variables that you put in in addition to the volume and the entropy when you talk about thermodynamics. You put in these same extensive variables integrated over whatever volumes are available. In other words, you sum over the volumes Vi and you get these various extensive variables for magnetization, the intensity of spins. For integral of density of spin or for the integral of some kind of species, that's what gives you these n variables that give the chemical potentials mu as their conjugates and so on and so forth. So these are the natural variables for coarse graining to define entropy in the density matrix rho. Now this is very necessary because you remember that we were talking about measurement in connection with decoherence and irreversibility. So we needed a natural set of variables for defining irreversibility in order to be able to talk about the measurement with these natural variables for habitual decoherence. But if we can define irreversibility with the same variables, because we're defining coarse graining for entropy with the same variables, then it's all in the family and we can do it in one operation. And that seems to be the case. That's what I say in this transparency.

32:30 So, we are recovering then an entropy with two principal terms in it, an entropy increase, one from the decoherence of the quantum alternatives P-alpha, and the other from the multiple configurations that give the redundant recording, and both of these, the second one may give a huge entropy increase. The first one may be very modest, like one bit, several bits, depending on what kind of measurement you make. Now, I apologize. For not discussing the timescales, we haven't looked into them carefully enough, and in any case there isn't time to talk about them, but there are. The whole thing that I've been saying makes sense, only if one specifies the timescale. The timescale for reaching equilibrium inside the volumes VI, the timescale for decoherence to be re-established, very short, as Jurek showed us. The time scale for the relaxation of the coherent matrix elements of Rho twiddle, which is enormously longer than this one, as we were shown in the previous talk, the time scale for the persistence of the mark, and then the aegis' time scale, which has to be matched to the persistence of the mark that it uses. And we hope to treat all these time scales for time, but we couldn't do it now. But we see, the main point is we see now that these quasi-classical operators And perhaps somebody can refine the definition of the set. We have only given a first cut at how to specify it. But these quasi-classical operators give us now a sort of classical world of the kind that the Copenhagen people of sixty years ago were sort of talking about. But there's two things wrong with the way they were saying it. There's no need for separate classical laws. This is all within quantum mechanics, completely within quantum mechanics. And second, these operators are available only because of the special character of the density matrix of the universe, and that's something that they were unwilling to do and which nowadays one can discuss. So once again, the resolution of puzzles in quantum mechanics requires not further agonizing scrutiny of the theory itself, but the utilization of the initial conditions for the density matrix. The environmental sciences depend crucially on these variables, the measurements, the results. It's the third kind of information about the universe in addition to H and Rho naught, but you get a lot of regularities for those alphas as a result of H and Rho naught, but the Rho naught is crucial here for that regularity, and it's the Rho naught that permits the regularity that allows the environmental sciences to be sciences. You father ammonite. You don't know that from Rho naught. You don't know that except from Rho naught. You don't know it because of H, and so on.

35:00 So, given quantum mechanics and given age, even elementary particle physics is now thought possibly to have some of these environmental parameters in it. That is, it may turn out that the curled up structure of the extra six dimensions or expected values of various fields in the infinite number of fields that go to make up the string field, many of these things might turn out, people think, people are afraid. They might turn out to be up for quantum mechanical grads. Now, this can happen, of course, through simply being dependent on the row of T naught or logically separate ideas. They can simply be quantum mechanically up for grads altogether and be alphas that we have to measure. They'd be different in another universe, but they have certain values in our universe. And elementary particle physics would be degraded to the status of an environmental scientist. It may be. And people will worry about it, and people are concerned that it may be so. Even in our universe, it's conceivable that these numbers could vary from reheating bubble to reheating bubble. And that would be even more interesting, because there there's not this absolute impossibility of the two coming into contact. Now, we learn about these things, these three kinds of information, in different ways. This does not require the so-called anthropic principle, which I would call an i-goosic principle, because I don't think people have anything whatsoever to do with it. For Ronaut, maybe, but it would be even nicer if Ronaut, as Hartle, and Hawking, and Vignenkin, and other people have suggested, is just some simple boundary condition the way H is some beautiful theory like string theory. So presumably H is string theory, and presumably Ronaut is some beautiful boundary condition for the whole universe.

37:30 Now, in the case of the alphas, of course, those we know only because we look around us. So for those, the igusic principle, or weak anthropic principle, or whatever you want, is perfectly fair game. Our existence, the existence of the other iguses, is part of what we see around us. And we can, of course, invoke it for the third kind of information, the alphas, which is part of that, part of that third kind of information. Now, the cosmological Now finally, let me say ten words about the IGUS. The IGUS has to be distinguished from simple IGS, information gathering system, like the MICA. That has non-commuting quantum projections correlated with commuting memory slots, uses amplification, preservation, macroscopic and permanent records, connects up with the NAI. All of that is done by the MICA. So the IGUS, the information gathering and utilizing system, has what special features? Well, maybe it can be gotten rid of altogether. I don't know. But for the moment, nobody has figured out how to live without a special description of an IGUS. So, for the moment, we have to live with it. And what it does is, in some fashion, however crude, it employs the fundamental formula based on Ro-naught, some primitive notion of Ro-naught, some primitive notion of the mechanics, H, and some primitive notion of prediction, which might be classical, but at least it's an approximation to the trace formula for the probability. Predictions are then made, and those predictions... Can be seen, empirically, from the fact that the igus engages in behavior. It engages in behavior which is apparently trying to control certain future perceptions. Perceptions in the case of an organism, or food, or sex, or whatever. Behavior that increases the probability, in other words, that the present data at some time in the future, the future present data, will include certain kinds of results. Or will improve certain kinds of results. Essentially, it's the thing that's betting on the basis of the probability. That is supplied by quantum mechanics. And it's hard for us to imagine those probabilities being utilized in the absence of something doing the betting. That's basically why we have to discuss the igus. It exists only because of Rho naught. Rho naught and H are such as to permit the quasi-classical operators

40:00 To permit the histories, to permit the decoherence and the associated coarse graining, the Ronaut is such as to permit information to be available in the universe and the igus lives on that information. We can list iguses in order of sophistication. The brilliant alien from the neighborhood of a distant star who regards this gathering with complete content. The human being. With mental faculties intact, knowledgeable about quantum mechanics, knowledgeable about cosmology, the highest form of life we can imagine, right here, using it to make predictions and to reconstruct history, or a normal human being ignorant of quantum mechanics, making predictions approximately, reconstructing history, not knowing what he's doing. Probably the big line is here! Then mentally subnormal human being, an anthropoid ape, lower mammal, goldfish, amoeba, and so on. Surely these are all, to various extents, iguses. Is there a threshold of complexity in order to discuss an igus? We don't know. I would think that it would be very much lower anyway than a human being, which is what most people seem to talk about as a threshold of complexity for an igus. It seems to me extremely unlikely that it has anything to do with being human. But what's interesting is that the IGUS seems to fit into the class of complex adaptive systems on which general work is now commencing with people observing common mathematical properties of these complex adaptive systems. So that a study of complex adaptive systems should include the quantum mechanical observer or IGUS. People have looked at the equations for an organism that learns and behaves, for an ecosystem, for biological evolution treated as a whole, population biology. The operation of an immune system in a mammal like us. Prebiotic chemical evolution, the evolution of the molecules that later gave rise to life. Also an adaptive complex system, very similar in fact. In fact, life can be considered simply as a continuation by other means of the earlier prebiotic chemical evolution. As far as those molecules are concerned, the advent of life is a minor incident in the prebiotic chemical evolution. Those molecules are still there, they're still evolving, they're using us for that purpose.

42:30 Computer programming, like John Hollams at Michigan, with random mutation and selection in the program, evolving new strategies that no person has ever thought of. Computers based on so-called neural nets, and so forth and so on. Where is the line drawn in this hierarchy of adaptive complex systems that would distinguish an eidus from a non-eidus? I have no idea. Maybe a thermostat should be allowed, too. I don't know. There are differences to the extent to which the various capabilities are hardwired or learned, and differences in the extent to which computation is obviously going on in the system. And these two things may be important. These two parameters may be of importance, but we don't know. Often claimed that an observer must possess a degree of sophistication comparable to that of a healthy human being with so-called conscious awareness. I don't know that that's really the case. But if it is, even if it is, the property of focal attention or awareness or consciousness in its form, various forms, psychologically it seems best to be identified as the one serial processing searchlight, like a mouse in a computer, serial processing searchlight on a web of parallel processing neural or mental activities, needn't be restricted to human beings, in some less sophisticated form that perhaps exists for other organisms and maybe for devices. And certainly possibly for devices to be developed in the future. So it's not clear to me that it's relevant. Anyway, I would like to suggest that this whole field deserves serious research by people not in their dotage, by people who are not cranks, and including even such far-out questions as the significance of the human subjective impression of free will. I think it's perfectly fair game. It may take us many decades to understand it, but I don't see why it should be not fair game for scientists to think about it. But in the meantime, what's most impressive, I think, I don't know if Jim agrees, what's most impressive is that the measurement situation, even in a simple system like fission tracks and MICA, already possesses most of the features that we are interested in for the physics part. The measurement situation, in other words. Thank you. If you identify as crucial...