Conference opening remarks

0:00 This is a re-recording of the Osgoode-Hill 1988 conference, Quantum Gravity, on General Relativity and on Quantum Gravity, which was originally recorded by John Stachel. It's being re-recorded here in Fougere on the 26th of February 2006, fortunately by a catastrophic error. I think because I pressed the record button on the most plain at the beginning of the first tape, John Stachels at the 1988 meeting have now been taped over, and that's a blizzard of sound, just a blizzard of static, he said that somebody, the recording, the original recording didn't catch the name, but I'm pretty sure it must have been... To be at the meeting, he thanked particularly Chris Isham and Ape Ashtekhan in making the intellectual arrangements, presumably securing the participation of the speakers, and I want to say a few words about the earlier meeting in 1986 and also the crucial one in 1972 with Paul Dirac. I think the only thing of significance that has been missed is his remarks about Penrose's absence, and thanks in particular to Chris Isham, and an apology to Bob Wald for having left his name off the list inadvertently.

2:30 He now comes on to say that there will be a change in the running order of the program on the Wednesday. There's another universe in which the sequence will be just the same, but unfortunately I cannot share that face. Clearly. Let me say a word about the Boston University Center for Einstein Studies, which is hosting the affair and putting the bill, most importantly. The center is the First of all, it's distinct from the Einstein papers, the Einstein publication project, which is a project of Princeton University Press and the Hebrew University, physically located at Boston University, but not the responsibility of Boston University. The Center for Einstein Studies is a center set up by Boston University and part of the university activities. Among the activities of the center are obviously holding conferences, usually here at Osgoode Hill. A publication, a project plan, which we call Einstein Studies, the first volume of which will be the proceedings of a conference held here in 1986, as far as we know, the first conference exclusively devoted to the history of general relativity, and that should be out this fall. And we hope the second volume will be the proceedings of this conference. You will notice there are microphones here. This is not to amplify voices. As I said to somebody before, anyone can't... speak loudly enough to be heard by 30 people should just give up. They're just here to enable us to record the talks and the discussion. We hope to have an edited version of the discussion appear in the proceedings so if people would be kind enough to announce their names speaking at least the first few times so that when we finally get down to recording this to transcribing this we can recognize the voices and the names. Other things that we the center does is sponsor visits.

5:00 Well, maybe I should go back to the publication. We're interested in publishing anything which can be remotely connected with Einstein. This includes scientific activities of Einstein, political activities, social, educational, anything which we can fit under that rubric, we would be interested in publishing. So if you yourself have a manuscript or know of anyone who has a manuscript in this very broad area, please consider publishing it in Einstein Studies. The name Einstein Studies could be used as a heading. We have had a number of visitors in various areas, not only scientific, historical, philosophical, one social. Somebody was doing a study of Einstein in relation to Jewish. So again, if you yourself are interested, or in Auburn are interested in visiting, contact me about that. Other announcements? If you have a long comment, five to ten minutes during the discussion period, please see the chairman of the session beforehand, if you know that you have a long comment. We have not been able to implement time reversal. And also, I ask the speakers please to try to observe the time limits, unless they are interrupted during the course of the discussion, we won't take that time off your time, but if you proceed without interruption to the end of your allotted time, that will be considered great help. This is actually, as some of you know, the second conference held at Osgoode Hill on quantum gravity. The first one was held here October 31st to November 3rd, 1972. I was sponsored by the IRS, which some of you may know was the Institute for Relativity Studies, which was an earlier avatar of the present Center for Einstein Studies. I couldn't think of another acronym that would fit so nicely as IRS, but it was a nice feeling having my own private IRS for a while. I made out a lot better there than with the other one. Among the guests at that meeting was one whom we shall unfortunately not see again, at least in this world, Paul Dirac. who spoke on his ideas about the possible difference between the microscopic and macroscopic metric tensor.

7:30 I also remember, and I was glad to see that Carol Kuhar spontaneously recalled it as well, a wonderful exchange between Dirac and John Wheeler on the question of what was the nature of the quantum principle. And I think those of us who remember that exchange still chuckle over it. And with your consent, I'd like to dedicate the proceedings of this meeting to the memory of... A number of the other participants in the meeting, fortunately, are still here. For example, he gave, to my knowledge, and he confirmed it, the first of his magisterial survey talks on general relativity at the Nubian. He confirmed that he gave the first. Magisterial is my adjective. Well, if we talk about length, he, I think, would agree magisterial was two hours. He was allowed two hours at that time. And we offered him four hours this time to report to us on the progress that had been made. In the meantime, he thought that was excessive, and he offered to give a ten-minute talk, but we compromised on fifty. Others that I remember are here, and I apologize if my memory has failed, are Bryce DeWitt, Jimmy York, Carol Kuhash. Some of the others who are not here today included Peter Bergman, Art Komar, Dave Finkelstein, Charlie Misner, Roger Penrose, and John Wheeler. John Wheeler's renunciation of the geometrodynamical program under the influence of Andrei Sakharov's ideas, which were fairly phenomenal at that time. And perhaps we can look upon this as a remarkable early example of the convergence thesis on United States-Soviet relations. And looking historically at the relation between general relativity and quantum mechanics, I think we can easily see that's been dominated by the struggle between the two imperialisms. This is a form of a nonlinear unified field theory, which is some sort of natural extension of general relativity, but ultimately be able to explain all quantum phenomena. And the other imperialism, of course, is the quantum field theoretic imperialism, which looks upon the field equations of general relativity as just another, perhaps particularly messy, example of theory to be treated by the established formalism, if established is the right word, and the interpretive schema of quantum field theory. And the first Osgoode-Hill conference was dedicated, at least in my mind, to an early advocacy of the doctrine of peaceful coexistence and competition between the two imperialisms and perhaps even to an exploration of the third ways that do not assume that either of the imperialisms will ultimately triumph, a viewpoint that was quite unorthodox at that time. Perhaps it's a little more orthodox to be unorthodox today than it was then.

10:00 String theory, for example, I think would fit under what at that time Roger Penrose in the session we had on alternate viewpoints called the crackpot theories. Since Roger was one of the speakers himself speaking on twistor theory, he had every right to use that term. I hope string theorists have an equally good sense of humor. Dave Finkelstein also reported, for example, on his space-time code approach. At any rate, I hope that the tolerant, non-imperialistic spirit will prevail here at the present meeting. As I regret Now, I didn't arrange for publication of proceedings of the first meeting. As I indicated earlier, I don't intend to make the same mistake twice, and Apai and I will be editing the proceedings. It would be a great help if the speakers could give us their manuscripts by the end of the summer, in which case we can guarantee publication by next summer at the latest. And of course we'll give everyone a chance to look at the transcribed version of the... Discussion comments so that you'll have a chance to edit it and take back all the things that you didn't mean to say and say all the things that you really meant to say but just didn't somehow get a chance to do well now excuse me pardon me that's a wonderful idea i think i'm high and i i can't speak without Well, it remains then for me only to thank you again all for coming and to turn the chair over to my dear colleague, Abner Shimani. Our first speaker this morning is going to be Wojciech Jurek, who will talk to us about quantum theory and measurement. Wojciech is very famous for his great anthology with Wheeler on quantum theory and measurement.

12:30 He's also made his own contributions to foundations of quantum mechanics. I think he is one of the outstanding environmentalists of our time. Well, environmentalist is one of the great causes of our time in other respects. And I think he has his chance to show that it can clean up quantum mechanics as well. Encouraged by these words, let me put a title about the ten points I've written out, emerging for consensus. In practical terms, this means that I know about five people. Who would be prepared to fight over these things? I can make this statement, there's no time in the trouble. I'm sorry? So you are joining. Having given the talks about quantum measurements quite a few times, I'm aware that sometimes one is not able, in spite of the emerging consensus, to get through all the transparencies. So I decided to write out basic points of what I'm going to say on the blackboard, so that they can... Act on your subconscious while I'm doing whatever I'm going to be doing. A very short abstract of what I'm going to try to tell you today is that the old correspondence, the old identification between quantum and classical and macroscopic should be, in the view of the consensus gang, Isolated and classical open. People who have perhaps started to some degree working on this subject include Professor Tse from Heidelberg, who wrote a very nice, very interesting paper on this subject by Tse and his students in the section of physics in 1985.

15:00 Professor Wigner wrote a very nice paper advocating similar views. I have written a number of times in a number of places and other papers which emerged more recently have to do with more specific applications of quantum optics. Let me go through the points of the consensus and see if we can agree on any. First of all, and that's perhaps the most controversial one, Quantum theory applies to the universe as a whole. We don't know really if when we understand quantum gravity, quantum theory will be the quantum theory we used to know. But I think it's good to try with the assumption that says exactly what it says and see if we can reconcile what we think we see with this assumption. Point number two, or point number one, given that this one is really a very basic assumption. This is an assertion that Copenhagen interpretation, as we used to know it, that is, division of the universe between classical observers and quantum systems, is inadequate or at least incomplete, because Copenhagen interpretation does not tell us how to draw the line between ones and the others. So we have somehow to supply the one. We also know from our day-to-day experience, really, that there are degrees of freedom inside that universe, which is presumably all quantum, which seem to behave... In an obviously classical manner. That is, certain superpositions which are allowed in principle and could be evolved very nicely by Schrodinger's equation don't seem to show up in practice. For instance, I'm not in a superposition of different positions. Consensus is starting, consensus is starting, consensus is starting to erode. Point number three. Big coupling. To a quantum environment can induce an apparently classical behavior in an open quantum system.

17:30 The way it happens is that this interaction with the environment has a character of a measurement in which the environment acquires the information, monitors a certain observable of the system. The observable that's being monitored usually satisfies a commutation relation. It's eigenstates or projection operators which are composed of its eigenstates commutes with interaction on a duct. In other words, the environment tries to perform a non-demolition measurement in the sense of cupcakes and chip corn on the system. Now, this monitoring by the environment can induce classical behavior. That's a method that is, for instance, it can make positions. It can ban superpositions of different positions of the same object. And I've been calling this effective superselection rule. It's not really a superselection rule because there is no in principle reason for phases between different positions not being there, but these phases are in practice inaccessible. Now, having said all that, we have to realize that the universe as a whole has no environment. So we can't apply this big mechanism to the universe as a whole. On the other hand, degrees, some degrees, within the universe can refer to other degrees within the same universe as the environment. So for some degrees within the universe, we can expect this environment to work. And the last point, and I think in many ways the very central point of this whole business, is that if one looks at it carefully enough... One gains the conviction that this whole story of measurement is not so much a story of preliminary equations and states and operators, but a story of information. That it's a fact that the information is being transferred in the course of interactions which makes systems behave the way they do, for instance, make systems behave classically. Now, I sort of used a jargon of Copenhagen, I guess, unwittingly or perhaps not deliberately in a couple of places. I think one can restate everything that I'm going to say in...

20:00 The language of any interpretation which is consistent with Schrodinger's equation. In fact, I think the interpretation that somewhat to my chagrin fits best what I'm going to do is manual interpretation. I'm not terribly happy with this, but I'm going to state that I know that that's without any apologies. So let me start by a summary of the measurement problem. And I'm going to rely here on the formulation of von Neumann. Measurement and quantum theory, a la von Neumann. The two systems, the two objects which take part in the action are the quantum system and the apparatus. Both are quantum. Each of them has the same number of states of business and idealization. We know that apparatus are generally big and have much bigger Hilbert space in the system. Von Neumann describes the measurement process is by splitting it into two stages the first stage of the measurement is when the initial state of the system which has some wave function fewer state psi which lives in the Hilbert space HS stand by eigenstates N gets correlated. With the state, quantum state of the apparatus. You know, the number of states in apparatus is wrong. In the denominator, there's only one state. I copied by me. But I knew that as soon as Murray was here, he would know. I might lapse again. Please forgive me. Let the record show. He points out to the macrons as distinct.

22:30 So I have the chance to edit. First stage of the measurement. The initial state of the system and the initial state of the apparatus before the measurement are a direct product. That's how they look like, written out in the basis that I specified above. During the first stage of the measurement, via Schrodinger equation, with an appropriate interaction, this initial state can completely legally, meaning within Schrodinger's equation, Which one can write out here. States in this basis N look correlated with the apparatus states in the basis AN. The coefficients stay the same. This is still a pure state. Now the ambiguity that I'm going to address, and that's really the main focus to some degree, what I'm going to say, is the fact that one can rewrite this pure state in an arbitrary basis. Now that's not always going to be comfortable, because if I take an arbitrary orthogonal basis, say for the apparatus, different basis from AN, the basis of state M generally will not be orthogonal. Now that's not that terrible, because we know that there are very decent non-orthogonal bases, for instance, coherent states of the harmonic oscillator. They are not orthogonal, and yet they are very decent and very widely used bases. So the ambiguity here is that we don't really know after the first stage of the measurement what has been measured. We could extract different sorts of information. In a way, and I'm going to come back to this, after the first stage of the measurement, all that happens is that we have an Einstein-Podolsky-Ozen correlation between the system and the apparatus. How come it is that experimentalists seem to know what their measures are? I'll try to explain next week. Second stage of the measurement. And that's where some more experimentalists know what they are measuring, is that this pure state by miracle, miracle meaning something that happens outside that is not accounted for by Schrodinger equation, becomes transformed into a mixed state.

25:00 Now this mixed state is no longer a projection operator. If we square it, it's no longer equal to itself. And it has presumably some definite diagonal, but this diagonal could have been either, in either of this, of, the second stage is a stage which is reversible, the second stage is a stage at which the real measurement is supposed to take place, the irreversible, indelible, no phenomenon is a phenomenon until it is a measured phenomenon, measurable. This second stage is called reduction. What one insert usually between one and the other are small screens like amplification or like irreversible. In a sense, one can model some of them, but in a sense, it's obvious that whatever, whenever we have to stick to Schrodinger's equation, we will have problems with trying to understand this character. The other thing that I should stress is that if one has this mixed state at the end, the mixture, probability interpretation becomes possible. In other words, we could say at this stage that actually the system is in one of these states, eigenstates, in one or the other basis, and we just don't know which one it is. At this stage we can blame whatever ambiguities there is about what has happened, not on anything fundamental but on our ignorance. At this stage we could not have had that before the reduction has occurred. So let me now state more carefully the problems that I'm going to specifically address. A big question, of course, is what causes the transition between the first and second stages of measurement. Some people could say, is this transition really necessary, in principle? A smaller question, which I'm going to...

27:30 More specifically, focus talk is into which basis does the wave vector collapse? That is really Bryce's question. How come if a company delivers an apparatus that is measuring positions of electrons or whatever it's supposed to be applied to, the observers are measuring the experimentalists? Can't say, aha, now the correlation has been established, let me look at it in a slightly different way, in a slightly different basis, and read out the momentum. Somehow this is impossible, and I would like to understand why this is impossible. Now, the answers that I'm going to suggest is that when a quantum system is open, and obviously this small space of an apparatus that I wrote out on the previous transparency is open to all the rest of it, There may be, and usually is, a preferred basis, what I'm going to call a pointer basis, because that's a basis in which pointers are going to exist, and interferences between these different positions of the pointer will not be allowed, and this pointer basis is chosen by the interaction between the Hamiltonian, by the Hamiltonian of interaction with the environment. They're not concerned about the environment. They're concerned about the system coupling that you want. They're concerned about the apparatus and the system, and that dominates everything else. They are concerned about couplings, and I think it will become clear. Those couplings which are important. Let me make sure I understand that the word detector, those together are what you're calling, I mean is that by itself open or are you talking about the environment being everything outside those two things? No, these by itself are closed. The environment is on the outside, and we need to appeal to something more in order to understand what is classical and what has been made, okay? And the real question is not so much about apparata. The real question is about things like chairs. Why are they in definite locations, not all over zero? And it's the same question. That's what really I'm saying. That's the basic point I'm saying. Why are certain observables classical? And what, what chooses a classical theorem? You're saying that all this time we've been subconsciously using the environment. Oh, yes. We're designing our apparatus now.

30:00 Why do you imagine that something has to be designed? There are lots of natural things lying around. Oh, sure. But... Nothing special about some of these things. If you want to do a Stern-Gerlach experiment, you have to build the apparatus right. Stern-Gerlach experiment is on my next transparent... Superpositions between the eigenstates basis of preferred pointer observable are destroyed. Classical. Let me just read it out. Now, there is still this big question that's looming there. And I'm not even going to really attempt the answer. You were saying something about the input. Here we go. Okay. I think one can try to analyze systems which are realistic and which are very hard to calculate and very hard to understand, but I think it's very good to start with a very simple system in which everything is crystal clear and see if anything of it works. The simplest possible apparatus will concentrate not so much on this big thing, Stern-Geller apparatus, magnets, etc. Incidentally, this is a reversible Stern-Geller apparatus, that is, spin enters here, would be split up and down, and would be recombined if nothing else happened, and come out in the same state as it entered if nothing else happened. Now we'll make something else happen. We put a one-bit detector. A two-state system along the upper trajectory of the spin, which is tipped off or rather kicked up if the atom carrying the spin passes nearby, so the transition that happens is from the down state to the up state. This has to happen without energy, so don't think about these things as energy level, but all that we are talking about is three-dimensional Hilbert spaces, so we don't worry about . If the trajectory that's been chosen by the spin is the down trajectory, then nothing happens to the detector. It stays in its zero state.

32:30 So now, let's be nasty and put the initial in the state pointing outside of the transparency. The initial state is here. That's before the first stage of the measurement. That's after the first stage of the measurement has happened. Well, we could say everything's already settled. We know that if we look and see the apparatus in the upstate, we'll be sure that the spin went along the upper trajectory, and vice versa, if it stayed where it was, then the spin must have been pointing down. First stage of the measurement is completed. Why do we need anything more? The correlation is there. The measurement has happened. Well, the ambiguity. Here it is. This wave function can be rewritten in a very different basis of the apparatus, basis of the states plus and minus, defined here. That's a very decent basis in a two-dimensional Hilbert space. There's nothing that could prevent us from doing this. So let's rewrite it, and after we've rewritten it, it will turn out that our nice, triangular apparatus with the magnetic field pointing up can be used to determine Whether the spin that went through it happens to have a state pointing quite perpendicular to the direction of the magnetic field. Now, this decision can be made after the spin is light-year away from the revolution of the Stalingrad apparatus. We'll just be determined in how we are going to look at the atom detector, the one-bit detector that's been sitting there. I've chosen point number one. There is no difference between this wave function and the wave function that appears in Einstein-Pilotsky-Rosen paradox. It's the same story. It's just a non-separable correlation that's been introduced by the interaction between the two.

35:00 To somehow think that the measurement will end here and after the measurement is done, all we have is Einstein-Pilotsky-Rosen paradox would be probably unsettling to experimentalists. We know it's not really a paradox. We know that we understand it all. We know it's a non-superbable correlation. We know there is no danger. But we still would like to understand why were we able to read off something which we should not read here, which in principle we didn't think we would be able to. So how does the environment help? So how much the environment can help us in resolving this problem? Well, let's enter the functions that emerged after we just established the correlation between one-bit spin and one-bit atom detector. And let's imagine this detector, one-bit detector, is now coupled to some other degrees of freedom, which we'll call environment. And let's imagine that this coupling is such that after the one-bit detector interacts with the environment, What happens to the total wave function of the system apparatus environment is that it goes into the state in which the state of the environment becomes correlated with the state of the detector. If the correlation is really nicely established, which means that the states up and down of the environment are all not orthogonal, Just carrying out mathematics, one can calculate that the joint density matrix describing system and apparatus is mixed, and it's mixed and diagonal in a very definite pointer basis, the up and down pointer basis, that we've chosen, or that the environment, or the interaction between the environment and the apparatus has chosen, and that has resulted in this side twiddle wave function. In other words, just substitute the choice of the basis of...

37:30 It's coming. It's coming. Interaction. So this is a preferred basis. Now what chooses this basis? First of all, one could say that nothing really has happened here except for a chain of successive measurements because all that really has happened is that environment performs the first stage of the measurement on the state of the apparatus. On the other hand, we recognize But we won't go chasing down the correlation in the environment. We have no other choice but really to trace out the environment and that will end up giving us a definite preferred basis of an apparatus that will always end up on the diagonal. And that's a basis that happens to commute with the environment apparatus interaction Hamiltonian. One of the conditions that one ends up talking about when one discusses this preferred basis is the condition that the eigenstates, apparatus, commute or approximately commute with the interaction, Hamiltonian, of the apparatus with the environment.

40:00 The measurement is done as soon as the atom has passed through the magnetic field because the spin is now stored in the vertical component of momentum. Now the coupling, if you look at the coupling between the spin and the apparatus, that involves the z component, the vertical component, existing. What the measurement is being stored in is the momentum, which does not compute. The basis does not, in other words, the apparatus... There are a number of different types of observables that are not commuting with the coupling in that case. It's precisely the conjugate variable in which things always get stored. And so I'm confused about this. And that's an example. I know what the coupling is. I don't know so much about it here later. This has me confused where you say that the bases of which are eigenvectors of some operator, that operator should commute with the coupling. It's just the other way around. The coupling of the apparatus with the environment, for example. The point is that the interaction of the thing thereafter with the environment wouldn't do that for one-dimensional mathematics. I'm not talking about mathematics, but that's the point of the question. Respect a certain observable. He's talking about the interaction of Hamiltonian. If you could tell me what the interaction of Hamiltonian with the environment would be, then I could maybe... The interaction of Hamiltonian with the environment would be right down, which has a form, some coupling constants, epsilon.

42:30 Other states of, let's say, some epsilon, epsilon prime, are basis states of the environment. So the point is that this interaction on its own leaves observable, which has eigenstates P, unperturbed during the measure, destroys superpositions between different eigenstates of the observable. Put it differently, if I were to write down, if I were to copy what von Meymann wrote down 50 years ago, for the requirement for the system to measure in a non-demolition fashion, Another system. I will end up with a Hamiltonian which is precisely this form. The environment is not measuring this specifically. It's just more degrees of freedom which brings about orthogonality. That's right. But what happens if you apply a general Hamiltonian, a general interaction, a general evolution, which will have the form power i-h-i-a-t to the state. In the case of the system initially not correlated with the environment, this type of Hamiltonian will make sure that it's this basis, which appears here on the arrow, that will end up appearing later on on the diagram of the mixture. So one could just say that this assumption is just a definition of a good apparatus? This assumption is a definition of a basis of the apparatus which does not get perturbed by the environment, in spite of the fact of the interaction. So, in this sense, it's a non-demolition measurement performed by the environment on the... Now, I'm going to discuss in a few moments more carefully a very specific example of this interaction. What happens if one uses position? We know that most of the Hamiltonians of interaction you sort of encounter in everyday world are a function of the position,

45:00 therefore they commit with the position. Therefore, position should be... is a good candidate for such a point you're observable. But before I get there, let's look at this whole thing that we've talked about so far from the point of view of information, because I think that's a very revealing way of looking at things. Let's look at the information transfer in course of the interaction between two quantum systems. Minus trace, row, log, row. Question? This part is certainly completed. You can add another thing. E prime. That's Hermitian construct. The only reason I'm creating this is that it seems like the underlying idea is that the environment makes it nice and the environment utilizes it. But usually, things like that from a modern model can make it better. And obviously, observing apparatus If you think you have a great journey, we'd love to talk to you.