Quantum State Reduction

0:00 So it's a very great pleasure for me to be here and honouring Jim Harple. I agree with all the wonderful things people have said about Jim, but they haven't said one thing about Jim, which I'm going to say, is he's a really nice guy. And that's important, because what I'm going to say in my talk is the talk isn't your problem mechanics. the fact that he's sitting there and nodding away with a big smile and saying that's Jim it doesn't mean he agrees I want to say something first about physics this century first of all there it is all these wonderful subjects one thing I did forget was a pointing device can I thank you They all have their problems, which I've put down. But special relativity, I don't think, particularly does. But general relativity, we know about the singularities. Quantum field theory has its infinities. And quantum mechanics, although not everybody worries about the measurement problem, I think that is a serious difficulty with quantum mechanics. I'm primarily going to be addressing the measurement problem, but it seems to me that all these things, at least from my perspective, are different aspects of the same missing thing, which is how you unite general relativity with quantum mechanics or with quantum field theory. There certainly is a view which is quite prevalent these days that the infinities of quantum field theory will be resolved if one finds the right way of combining quantum mechanics with general relativity. nowadays people talk in terms of string theory and so on but the idea really goes back to Oscar Klein finding a cut-off at very high momenta and so on very small distances and that perhaps that will produce a finite theory if one knew how to do it the singularities are accepted as something where say if one is going to come to terms with it somehow it's going to be in some unification between generality and quantum mechanics problem is not always thought in that way but I want to try and argue that this again is something which should come out of the appropriate union between these two subjects

2:30 people would normally use the term quantum gravity I think it's a slight misnomer at least from what I want to say because it tends to mean the appropriate application of quantum field theory to Einstein's general relativity or perhaps to some modification of Einstein's general relativity So people don't tend to talk in terms of modifying quantum mechanics or quantum fuel theory. This is not the usual perspective. On the other hand, my own opinion is that what we're really looking for is some more even-handed marriage between quantum fuel theory and general relativity, which will involve some gear on both sides, so that we need to modify the rules of quantum mechanics, and that the measurement problem, to my way of thinking, It involves a change in the rules of quantum mechanics. That's not the same kind of change that Chris Isham was talking about, although perhaps one can see some ways of bringing these ideas together. As you were saying, the Gell-Mann and Hartle point of view is a change in some respect. I think what I want to say is a more radical change from the standard view. Why does one perhaps need a change? Well, in order to address this question, let me first talk about the one area I think that people really do agree requires some kind of union between general relativity and quantum mechanics, namely dealing with the singularities of cosmology and in black holes, that somehow these singularities would be got rid of in some sense or made into a handleable physics if one had the right theory. and this would involve a union between these subjects. Here we have the standard cosmological models. Now, my view is that this is slightly misleading if we knew how to handle these singularities. What we really need to know is how to handle something a bit more realistic, which does involve a severe difference between the singularity we expect to have occurred in the Big Bang and what would result if we had a closed universe of all sorts of black holes, if we have an open universe, then we have final singularities in black holes, here we have a tiny sketch of a black hole, but this singularity is of course something where things get sucked into, it's like the time reverse of the Big Bang

5:00 in a sense, but our expectations are that it's completely different in detail, and this has something to do, or a lot to do, with the second law of thermodynamics. So I want about the second law because it seems to me that this I didn't put it in my picture here I think the second law thermodynamics also is something which is a manifestation of this appropriate union between these subjects here let me say a bit more about that now to talk about second law one needs really I mean talk about phase space now this phase space is really meant to be the phase space universe. Now people sometimes worry about that because they think well the universe might be infinite and so and so but something wrong with phase spaces being infinite there's not really anything wrong with these volumes. I should explain these things that are coarse grainings. The idea is that you imagine your phase space is divided up into a number of sub-regions that's the coarse grainings such that if you had any two points in one of these same regions you would regard microscopic, variables are concerned identical. So it's a sort of crude way of talking, in a sense, and you might imagine the coarse graining would be different from one person to another, but it doesn't seem to make that much difference, mainly because of the enormously different sizes of these volumes. This picture of mine utterly doesn't do justice to that. You have to imagine that if I move from one of these slightly smaller to a slightly larger volume, the factor of proportionality might be something like 10 to the 20, or something like that. So they're vastly huger. And for such vast changes in dimension, it's pretty non-critical about where you draw these lines. So in a sense, why the second law really works, even though it seems to involve this rather subjective idea, seems to stem from the fact that these volumes are so grossly different. Now, here I have a little yellow region here, which might be where we find ourselves. I want partly to address a sort of anthropic argument, because sometimes people say, well, in order to have people around, you've got to have a second law of thermodynamics. It seems to me that that's a bit misleading. Well, first of all, let's forget about the people, and suppose we have, I should say, in this description,

7:30 a bit, one has to cheat a bit, in that although to discuss cosmology one should be talking about general relativity properly, nevertheless I'm going to pretend that you can get away with thinking of this as having a time description. So the points in the space space are roughly speaking three-dimensional data and this will evolve in some way according to Einstein equations or whatever fields that might be present as well. So we're thinking of this as an evolving three-dimensional situation, although that's, you know, not completely satisfactory. But I think for this discussion, the reason that the way in which it's unsatisfactory is not important, although one might argue about that. Now, if you just imagine a random universe, well, it's likely to be pretty well in this huge volume. I call it thermal equilibrium, but when one talks about black holes and so on, you might find really got a huge black hole in it, but it's the maximum entropy, that's the essential point. And the volume for maximum entropy is likely to be so huge that it completely swamps all the others altogether. So that means that if you think of some kind of random evolution, it's likely to find itself either completely in that, or it might sort of dip down into one of these smaller volumes like that. But that's the sort of thing you would expect for a generic universe history now suppose you say, okay we're here, we're sitting in this room, we're organized things, we have minds and we must be organized in a certain way we do physics maybe takes a certain amount of organization to do physics, so you've got to pull yourself down into that region, this region is where physicists can be if you like and so this path goes something like that, well let's But if you put that in general position, because of the hugeness of most of these volumes, you'll find that not just in the future, that's the second law. That's fine, we know about that, we understand the second law is somehow because these things wiggle their way into bigger and bigger volumes. But likewise, into the past, you would find that too. You would find nothing like the kind of universe that we seem to perceive. the second law would go the wrong way in the past that's the most likely way in the absence of any other constraints the most likely way to have got to any situation like all us being in this room here

10:00 the most likely way is all sorts of particles or something came in from outside and created this not the way it happened the way it happened as we know from looking out in telescopes and measuring black body radiation and this and that has to do with the fact that there was a big bang okay, you see here's T equals zero Here's the Big Bang. So you have to turn this. Somehow, we're only looking at histories in which it started at this little tiny volume, which was the Big Bang. And one can make estimates of how much smaller that is than this from knowing how big the thermal equilibrium state is by looking at the Hawking, Freckinstein-Hawking formula for the entry of black holes and making estimates for how big this volume should be. and one finds that it's ridiculously enormously larger than any of these other ones and certainly than the Big Bang one. But you see that for a second law to have happened in the past this has to find its way into smaller and smaller and smaller and smaller volumes into a tiny, tiny volume which represented the smallest entropy that our universe has ever encountered. a lot of people try to explain say the uniformity of the universe and so on in terms of it's an idea I suppose I know that Charlie Misner talked about it I don't know where it went to originally referred to as chaotic cosmology the view being that somehow the universe started off in thermal equilibrium and we get all the things we see because of some processes which took place after that. You have to try and argue that maybe combining with the anthropic principle, you've got to have us here around thermal equilibrium. Well, it doesn't really give this. You think you get something more that way around. So I don't see how these arguments work. One sees this again in the inflationary arguments, and it seems to me they all suffer from the same problem. Whether they're right or not, that's a separate issue. The point is that they're not an explanation of what's going on here. explain the fact that the universe did start in a very special state and if we don't make that assumption we don't get a second law of thermodynamics which went back right to the beginning it seems to me it's a completely clear statement but if that's the case and it does seem to be the case

12:30 then we have to come to terms with the fact that whatever theory it is these are things I've said many times before but let me say them again we have to come to terms with the fact that the singularity structure in the universe, as we know it, whichever of these models it happens to be, it seems that it's more likely to be that one. That's the k equals minus one model, but it doesn't make much difference. But the singularities that you find at the future endpoints of people's experiences, as opposed to the past, I don't mean people, the future endpoints of world lines, if you like, as opposed to the past endpoints, these singularities are completely different in structure. as opposed to some very special nature here, and one can even make a good suggestion as to what the nature was in terms of vile curvature being restricted to be very, very small by comparison with other kinds of curvature. So whether that's exactly what happens or not, we're not sure, but something like that happens. And that tells us, it seems to me, that whatever theory it is which should be dealing with these singularities, and that should be so we say I mean I said at the beginning that what's accepted as a union between these ideas should be what deals with the singularities that union therefore must be a grossly time asymmetrical theory I've said that many times but let me say it again I think it's a good indication that the theory we seek is something which is not simply combining well combining like two time-symmetrical concepts. It's something that's going to involve a change in the very rules of quantum mechanics. So there's another argument which I sometimes put forward, and let me briefly mention it. I don't want to say too much about it here. And this is how one obtains probabilities from quantum amplitudes. Okay, the ways in which one calculates amplitudes reversible. These things will work one way or the other way in time. But what you do with the amplitudes is another matter. And here I just have an example with, say, source here and a detector over here, maybe sort of parabolic mirrors or something. And here's the ceiling in the floor. And here we have a beam splitter or a half-silvered mirror in the middle. And we imagine that whenever this thing emits a

15:00 photon, it's registered somewhere here, and the detector will register if it receives photon, and the two things that it might do if it emits one is go this way, the other is that way, amplitude one over root two for each, take the square of them, you get the probability that it's half that it comes here, half the other time it goes into the floor. That's fine, that's the right answer, but if you try and read this very same experiment in the reverse time, that is to say you ask a question, suppose the detector receives the photon, a photon, what is the probability that it came from the source? I'm not reversing the experiment, I'm just asking the question the other way around. If the detector registers, what is the probability the source did? It can go through the same thing, calculate amplitudes, 1 over root 2 all over again, 1 over root 2 coming from the ceiling, 1 over root 2 going straight through, and that amplitude calculation is perfectly right, but when you square them and you get a half a half, that's completely the wrong answer. The right answer is it's almost certain that it came from the source, most unlikely that it came popping out of the ceiling and some people when they see this argument say oh well you should take into account second law you should take into account this and that and the other thing ok maybe you should to get the right answer backwards but what's remarkable is that you don't have to worry about any of those things when you do it in the future direction the future probabilities come out right simply by doing the nice beautiful simple squared modulus rule of quantum mechanics a miracle but it comes out right direction, and it doesn't in the past. Well, Jim would have some other way of talking about this by putting his particular state at the far end and so on. But I'm not, I mean, you might treat this thing in a different way. It seems to me that at least what's said here is correct. My own interpretation of this is that it's a sort of complementary feature to what's going on here. and although again it's not something I want to say a great deal about because I want to spend my thought mainly on other things but these are sort of inputs to the general conclusion at least my conclusion that to understand the reduction of the state we're going to have to understand it in the context of combining general relativity to quantum mechanics and what this discussion that I just very rapidly

17:30 telling us seems to me that there is something time asymmetrical involved in the measurement process, not just that you have to be irreversible things here and there or something, but the actual way in which you work out probabilities involves an asymmetry in time. And that to me is the other side of the coin to the specialness of the initial state and the second law of and the fact that black hole singularities are generic and so on, and this is all interrelated to the Hawking evaporation of a black hole and so on. And again, although it's not something I want to go into detail, I'll just mention it rather quickly because it seems to me it's part of the whole story. Here one imagines a black hole which is formed by gravitational collapse. it then radiates Hawking radiation until it loses all its mass after goodness knows how long finally disappears in an explosion and then particle physicists all worry I wouldn't say all of them but a lot of them do about the information which appears to be lost in the black hole or is it in fact retrieved in the final explosion or is there perhaps some final nugget which just hangs around and sits there and contains all this information that was sort of absorbed in the beginning here. Stephen's view was more or less that the information is lost, and I've always been in agreement with that, but I tend to go a little more further with that and do something that he wouldn't like, perhaps, namely that there is somehow an actual loss which has to be retrieved in the measurement process. So here I just consider this sort of Hawking box where you have a material inside this, and here you have a large entropy region where there's just a black hole sitting there in thermal equilibrium with the material, and the other situation, a large entropy, a large coarse-grain volume, where you just have gas running around, and you just look at the, you just wait forever and see if it sort of goes between these two different states, and you follow the point in the phase space and it comes around and according to what I would claim it seems to me that definitely you get something lost not only is it information lost but in some sense

20:00 the phase space volume of course it has to be really a quantum picture or a classical picture so it's not really quite clear how you should use this argument but it's roughly speaking that you get more arrows coming in than leave it so the more different kinds of states can produce lots of different things to produce one thing at the end and that's all to do with the black hole being such a huge entropy and so on but then if you sort of chase around this picture where does it all disappear so or does it come back again and the argument it does come back again but it comes back again in the state reduction process and the asymmetry in time has to do with the asymmetry that i've just been talking about here so that in principle one would have a balance between the caulking evaporation from black holes and the rate at which state reduction takes place. I've suggested this idea a long time ago, occasionally suggested to a student that what normally happens is they would give up and leave the university or something. So I sort of keep it to myself. Someday maybe I'll have another go at trying to make this into a quantitative argument. Seems to me it could be made know how to do that just yet. Okay, now let me more directly talk about the state reduction problem, which of course is usually talked about in terms of shredding his cat. I know Stephen doesn't like people talking about shredding his cat. More than John Bell, he talks about shredding his cat with the full cat and the empty cat, if the cat has had its meal or hasn't had its meal, which is a more kind of a nicer way of talking about about people shooting each other, though. It seems to me, if you were going to not allow the cat to be killed off, why did he allow people killing each other? You know, it's a bit more hypothetical, of course. So I'm guessing he was shrewding this version, except he didn't have a gun. He had poison, but that's not much of a difference. So here I have a photon coming through. It's putting a beam split into a superposition. It's two different states here. one of them triggers a device which fires a gun and kills the poor cat the other one leaves the cat alone and if you think of the unitary evolution of the entire system, you're left with the cat being in a superposition being alive and being dead and it's the sort of thing you have to take seriously because suppose you didn't do that but put some mirrors here

22:30 and another being splitter there then you know that both roots have to be felt out by the photon because interference here and constructive interference this way that the photon would always come this way if everything was perfect. So somehow the photon does have to feel out both roots how does it know it's not going to do this as opposed to this it has these fundamental problems of quantum mechanics Now, there are all sorts of arguments people put forward to suggest quantum mechanics shouldn't you'd have to worry about whether you can do this in one way or another. Here's just a picture to show you that if you have quantum mechanics, something that everybody knows is quantum mechanics, like a spin of a spin-half particle, then you take all the linear combinations and you get every one of these states is just as good as each of the other. It just depends on how you define your basis and so on. What's so special about up and down? Well, nothing. But if you start applying that to cats, and people start worrying. So here we have live and dead as the analogues of up and down, live plus dead, live minus dead, analogues of right and left, and live plus I dead, and live minus I dead, and so on. And so why don't we have all these different states just as much, sort of, manifestly as these ones? Now, I don't want to go and talk about all the conventional arguments about this. I've never had time to talk about mine. I will just waste something, just because I don't want to waste this transparency here, which I used for another lecture, but let me just say it anyway. And then I'll get on to the more business stuff. So here we have an EPR situation in the original Bohm form, where we have a spin zero initial state, two spin half particles going off to opposite corners of the room, and you might make measurements here and there. And the thing is that one has to consider the total. is a holistic thing which involves both particles together and you can write it as up here, down there minus down here, up there but you could also rewrite it as right here, left there minus left here, right there and so on and you could imagine, for example that a measurement might be made in some direction there

25:00 and that seems to put the state into the opposite configuration over here imagine that there was on the moon or something like that and then uh somehow you you might not know what they're going to do on the moon and then you have to consider that it's a probability mixture up and down or right and left it doesn't make any difference or you might use a density matrix to describe that um okay i'm going to apply the same argument now to people when they talk about decoherence seems to me it's very similar to this situation because you hear you have a live cat together with its environment and a dead cat together with its environment they might be more complicated situations than what I'm actually describing here but this is just to get the point across but of course we could rewrite this one as combinations of alive and dead it doesn't really tell us anything special about live cats or dead cats, as opposed to live plus dead and the live minus... I had a bit of trouble drawing it so you could tell one from the other, but if you look carefully, you'll see these aren't actually quite the same. One's one plus the other, and the other's minus the other. So what does the environment have to say that makes the cat do one or the other? Just because the density matrix might be something or other, it doesn't seem to me enough. It doesn't tell you that the cat is one or the other. if you follow these arguments through it seems that you are driven finally to considering that the observer who comes along and looks at the cat, where there's an environment as well, also might be if you position and you look at the cat and then you think of yourself as being one of these people, notice that this person is perceiving here a live cat this one is perceiving a dead cat because of the bubbles over at the top here but you can see externally this space. So you don't have to worry about whether mentality can actually be represented as the quantum space or not. So you just look at the person's expression. And here are these. I can rewrite that stage in this way with linear combinations of miles and frowns and so on. And it seems to me that it doesn't really explain anything at this stage. You could argue that I should take a more general situation too, but one can apply this type

27:30 of argument, even much more generally than I've given it here. You might say that, well, there's something special about perception and that people are only allowed to perceive one thing and not superpositions, and evolution is given this like that or something. I never could see that argument, why you can't have, say, a state of perception which involves superpositions. You don't know what perception is, so why shouldn't these things also be perception states? Until we have such a theory of what is, seems to me, this argument doesn't actually go much further than this, and it isn't really a resolution of the problem. I prefer to look somewhere else, somewhere else, and that is that perhaps something goes wrong with the superposition principle when it applies to significantly differing space-time geometries. So here I have a linear superposition between two different space-time geometries, and the argument would be that in some sense this one or the other, and that there is some kind of preferred basis, if you like, which has to do with the geometry of space-time, that nature doesn't like to be sitting for too long, at least, in a superposition of different geometries. So that's the idea. A little bit more specifically, I call it objective reduction, which has the nice acronym of OR, that's OR, the other becomes one, or the other, which is handy to remember if you don't know. So here, I'm replacing the cat. I'm going to take a leaf out of Chris's book and cover this up a bit. Instead of the cat, I'm just going to consider a lump of material. Seems to me the cat brings in all sorts of irrelevances, such as the thing that Stephen objects to, like it might have its own mentality and one might worry about killing it off so why don't we just move a lump of material from one place to another, if the photon comes this way if it goes the other way, you leave it put where it was so that we have involved in the entire state a linear superposition of this lump of material in two different locations I want to raise the question of whether this is a stationary state there were just one lump and it might just be sitting there on the ground or

30:00 something might sit here it might sit there and you could imagine that either of those would be a stationary state I want to consider a question of whether two positions are stationary states now in ordinary quantum mechanics you would have say the position of a lump in two different positions and you have in the a D by DT, which I'm thinking of as a killing vector in the background space. So they could be sitting on the Earth, but these lumps themselves are supposed to be not significantly influencing the background geometry. Then you have each one of these in an eigenstate of this D by DT operator. And if these energies are the same, then every linear superposition would be also in eigenstate, generosity here. But what I want to worry about is if we bring in the gravitational field of the lump. If we bring in this gravitational field, does it change the situation in a significant way? As a sort of picture is concerned, let's go back to this one. This is the sort of thing you would imagine in space-time. Here is the lump in one location to begin with. Here is the instance of it which remains put, stays put here's the instance of it which gets displaced from one position to another each of these does slightly distort the space-time so we have a superposition between two slightly different geometries and the question of whether this is a stationary state or not raises the issue of how does one ask the question of whether something is stationary in a space-time which is a superposition of two different space-times and that seems to me that when it's beginning to encounter a tension between the fundamental principles of general relativity and those of quantum mechanics. And I want to say a little bit more about that in a minute. But my conclusion will be, let me just tell you that first, so let's see where we're aiming. The conclusion will be that the superposition is not stationary when you bring the space-time geometries in, but it's something which is a bit like an unstable nucleus or something into one thing or another in a certain length of time that one thing or the other

32:30 that it might decay into are the individual locations here or here. And I consider a certain energy which I'm calling EG, which is the gravitational self-energy of the difference between the mass distributions of the two states. So if a lump is over here, there's a certain mass distribution. If it's over here, there's another distribution. I subtract one from the other and then I work out the gravitational self-energy of that difference and I call that EG and I claim that that EG is some fundamental uncertainty in the energy of the superposition and in accordance with that although it's the other way around when you usually think about unstable particles one thinks of if there is a time of decay that has to be related to in the mass or the energy reciprocally with Planck's constant in it. So basically you have this formula here, which is, I'm reading it the other way, I'm saying that with this fundamental uncertainty, there is an instability, that is to say there's a decay time, a half-life, if you like, which is of the order of H cross divided by this energy uncertainty, EG. So that's what I'm trying to say we should consider, I should say that Deyoshi put forward an idea very similar to what I'm saying here, somewhat before I did. He had a slightly different perspective on the whole question, but he certainly also considered this. Now, the basic idea will be the following. You see, if we have a superposition between two... So let's start with the lump in one unambiguous location, and then we have an unambiguous notion of what you mean by d by dt, which is schematically indicated by these arrows here indicating this killing vector. But if we then pull these things apart, you see these killing vectors don't match. And there's a question about how do you say that d by dt, I mean, how do you even write down the Schrodinger equation? they're two different notions and you could say that they're two different notions actually onto two completely different space times and that is the correct if you like quantum gravity way of looking at it and you look at abstract superpositions of these things

35:00 and it gets a bit lost it's a bit hard to know what you mean by the time evolution of this system here but I'm going to take the point of view that there is a conflict between the principles of general relativity and those of quantum mechanics conflict arises sort of here because you might try and identify these two spacetimes. Here we have the two. This is more or less just what I was saying before. These are the two spacetimes. I might try to identify them but I know that because of the principle of general covariance I'm not supposed to be able to label the points on these two different spacetimes. I'm not supposed to be able to say which point here is to be identified with which point there. There's a sort of fuzziness about this very notion. Einstein says We shouldn't even say that it's meaningful to identify these points. Nevertheless, you might say that, well, it's not so far off. They're pretty flat, these spaces. Maybe one can at least approximately identify them and introduce some error. So that would be my point of view here. I'd say I'm going to try and identify these approximately, but that there will be some error, and that that error will be something that I can identify with this EG here. There's a fundamental uncertainty, which comes about because of this fact that we have this conflict between the principles of these two great subjects, and the argument would be, although these things are never utterly clear, and different people can have slightly different points of view on this, and Joy Christian, for instance, has certainly discussed this a lot, because I want actually to talk about what one might call the Newtonian approximation here where you can think about the speed of light going to infinity whereas you still retain some of the ideas of general relativity. This is basically the Cartan idea for looking at Newtonian gravity as a geometrical theory where the principle of equivalence is fundamentally built into it For example, a uniformly accelerating, sorry, a completely uniform field of Newtonian gravitational force would be identical to no field of force at all. You just fall with it, and that's equivalent. So you can bring in at least some aspects of the principle of equivalence, principle of general covariance, into Newtonian gravity,

37:30 and that's the sort of thing that I want to try to do here. But there are different perspectives on this, and I don't want to claim that you're driven to my own perspective on this picture. But it does seem to me at least a point of view which I would regard as being something, at least respecting the principles of general relativity as much as I can. What one tries to do here is just a Newtonian version of GR. we have here the Newtonian potential which appears in the time component of the metric and the question is when you try and identify you might think what's the problem in Newtonian theory because after all you've got a universe of time so what's wrong well what's wrong is you've got a universe of time but you haven't got a universe of v by dt v by dt of course needs to know what's being held constant it needs to know the x's and so if I shift my two spaces to respect to each other which I was doing in this picture let us say this way not that way I have a problem about identifying d by dt so d by dt needs to know partial d by dt needs to know how I'm going to identify the xd and so I claim there is a measure of uncertainty in making this identification my point of view is to try and identify as best one can the free fall so I'm trying to say that the Einstein would tell us that free-fall is natural, and so that you're trying to identify free-fall in one space, at least locally as best you can, with free-fall in the other space. And so trying to do that, but you can't do it without sort of spoiling the geometry, but you can estimate the error involved in simply gluing them flat together again, and the error comes out as this expression here, and then you integrate that, the square of that over the whole of space, and to integrate by parts, I had before, the gravitational self-energy of the difference between the two mass distributions. And that I regard, then, as a fundamental uncertainty in the energy of the state coming about, if you like, not because of the right-hand side of the Schrodinger equation, but coming about because of the left-hand side. You don't know what D by D T means. Okay. That's the general idea. How big are effects like this? Now, you might tend to think, goodness me, it must be ridiculously, trivially tiny. Who's ever going to worry about a thing like this? After all, gravitational effects

40:00 on a speck of dust or something which one might worry about. In fact, I'll talk about specks of dust in a minute. Surely the gravitational effect is going to be so small you're not going to worry about it. Well, it's not so obvious because people think gravity is small because, well, the Planck length is small. The Planck energy is huge, on the other hand. Whereas the gravitational energy you're talking about here are very small compared to the Planck energy, but they appear on the bottom of the formula. So that means you've got a small energy on the bottom. That means a long time scale. But a long time scale, in what units is it long? Well, it's long in Planck units. And Planck units are 10 to the minus 43 seconds. and that means that you can have something which might be a quite reasonable time period so let me show you this is the basic idea again so let me not talk too much about that if I consider a nucleon as just a uniform classical uniform sphere then I would obtain something like 10th of 7th years that is to say if it's in a displaced superposition two places at once how long would it take to go to one or the other something like 10th of 7th years which is fine because, well, people have done neutron interferometry experiments and they haven't seen this effect. Fine, they shouldn't have. If they'd seen it, I'd be worried, because it shouldn't be that quick. Nobody's held neutrons in superposition for that long. What about a little tiny droplet of water? Well, if it's about 10 to the minus 3 centimeters, you find it's about a millionth of a second would be the decay time in this scheme. A micron, about 20th of a second, 10 to the minus 5 centimeters, of hours. So you see the turnover is somewhat in this kind of range here, which is not totally unreasonable. Something you have to bear in mind, though, and that is that normally there's an environment entangled with the system, and that it may well be that in most situations of interest, the main displacement of material is in the environment and not in the system, and you then, basically, as far as I can see, get agreement with the standard decoherent people have, you lose information in the environment and you lose track of it, because on that scheme you never actually lose it, but here you lose track of it when it's in the environment you do actually lose it, because when the environment, there's enough movement of material in the environment that will cause the reduction and it will

42:30 carry the system with it. So the reduction might take place faster than the figures that I'm giving here. But if you're going to design any kind of experiment which is to see whether this effect have to reduce the environment effects down to practically nothing. is it a feasible thing to do in an experiment? Well, a couple of years ago, I visited Anton Dalinger in his group, as they then were in Innsbruck, and talked about a suggestion for an experiment, thinking that it was so completely off the wall they would probably laugh me out of the lab. They actually were rather surprising about taking it seriously. A lot of from Ralinger's group. I should also mention Johannes Duprich who actually suggested part of the idea I'm going to tell you about here. I'm supposing here we have a source of particles. Let's call it a photon. But there may be some problem about it actually being a photon. But let's say it's a photon. Here we have a beam splitter. It's going this way and this way. It's just very similar to the example I gave you before. It hits this crystal. crystal is something like about the size of a stack of dust or so. It has to be something like a MOS bar crystal so that the impact of the photon moves the whole thing rather than setting up internal vibrational modes or something like that. It has to move as a whole. And here I have the nuclei, sort of drawn schematically here, and this thing is put into a superposition of being in the original position and being in the displaced position. The kinds of figures that Zaliger and his group suggested were something like 10 to the 15 nuclei, and then the reduction time according to my scheme would be about 10 to the second. So here we have what you have to do is to wait to 10 to the second to see whether it goes to one or the other. And that means you have to keep the two parts of the photon here coherently for something like a 10 to the second. And Then, after 10 seconds, this is sprung back. There's a restoring force here. It brings it back to its original position. At that point, you release the photon here. It kills off the momentum, so the thing is just the way it was before, as though nothing had happened. Comes back. This one comes back, and you see whether there has been any loss of phase coherence

45:00 in the process, in which case they just come out this way. A detector sitting here would see nothing. However, if the thing reduces according to my scheme, then it will be one or the other in about that period of time half the time you'll see the photon coming the wrong way of course you might have decoherence of all sorts of other things it might hit an air molecule and you might lose something in the spring goodness knows what so you've got to make sure all these other effects go down to sufficiently low level that you can pick out the signal of this if it's there from all these other kinds of decoherence I would imagine what you do is you change these materials, try it with all sorts of different things so on, different nuclear concentrations, this and that, and you see whether you can pick out the signal of this particular suggestion from all other forms of decoherence. A big problem with this actual setup here is that to get this thing to move this amount significantly, so the nucleus has actually moved like that, this has to be an X-ray photon. This is an X-ray photon, you've got to keep it going for a tenth of a second, which is I understood from Dierlinger that it was not totally impossible with known technology, but not something that he wanted to do, which is saying a lot. Here's a suggestion, where he would, first of all, send one photon in. There you have a half silver mirror, a fully silver mirror here. And what you do is you wait to see if it comes out here. If you detect here, that means this thing has been put into a superposition. If you find it coming this way, this is in a superposition. air for a tenth of a second, then you send another photon and see whether you can pick up a signal of whether it has actually reduced or not. It's tricky in all sorts of other ways, so I'm not convinced that it's an improvement over this version, but it's an ingenious idea, which I hope will be considered in conjunction with this. There is another way that you could imagine keeping an X-ray for this long. Other things you might do is not use X-rays. You might use neutrons or that sort of thing. But you might think of using X-rays, and not do it in the lab, but do it out in space. But then you could have a platform here where you do one half of the experiment, and you have some mirror up here, about an Earth diameter away. It takes the light about a tenth of a second to go an Earth diameter and back again, and there is your way of keeping your X-rays coherently.

47:30 One of them is making a mirror, which will do this for you. They do exist. the idea was that one might be able to piggyback on the test program of Constellation X which is actually I should call it a telescope really it's an X-ray telescope which is usually put up in something like 2010 and there is some version of this which would try to do X-ray interferometry but I think it's not clear that that would actually be done but that's the sort of thing one would need something very similar to that in doing this It's being explored, and I don't know whether it will go ahead or not, but at least it's a proposal at the moment. There are other ideas. When I was in Santa Barbara, it was suggested to me. You might imagine some system where it's just represented here schematically as a blob at the end of a little whisker. Classically, it could be either one way or the other. quantum mechanically you might find that the minimum energy is superposition either one plus the other or one minus the other and you might take a situation where the quantum oscillation time the funneling time to go from one to the other is some kind of order comparable with the gravitational reduction time. I think twiddles here doesn't mean probably equals. I think the gravitational reduction time could be a lot longer but it needs to be thought about a lot to see whether an experiment of this nature could be done apparently there are some things of this nature which have puzzled people for a long time, such as molecules which exist in two mirror image states, and they ought to be in quantum superpositions of one or the other, and instead you find one or the other, not superpositions, and people worry about this, and is it something to do with electromagnetic effects of being in different Hilbert spaces and so on and so forth, and maybe it's nothing to do with this I believe, that remain in those, these situations. And it would be interesting to explore that more to see whether a test of this proposal can be found along these lines. I want to end by, when did I actually start? So I just wanted to, how much time? Okay, so I take it that means I've got another few minutes. Okay.

50:00 there's an issue which I very much skimped over here which one really has to worry about seriously and that is, what do you consider the mass distribution actually to be? You see if you thought about the quarks or say the protons, or worse, the quarks say, or the electrons, which are supposed to be point particles so any ridiculously tiny displacement would already give you an infinite gravitational self-energy put that in this, you would get, the decay time would be zero, you wouldn't have any quantum mechanics. So that can't be right. So what do you do? What do I mean when I talk about the mass distribution? Well, what I mean is that I consider this system here to be a solution of the Schrodinger equation, which is stationary. So the locations of these nuclei and so on. There will be some kind of a spread like this. For each nucleus there will be some hump like that from the mass distribution which will involve the jiggling motions of the particles and so on, but it's kind of average which comes about when you solve the Schrodinger equation for the whole thing and work out the expectation value of the mass distribution with respect to that solution for Schrodinger equation. You will also have to include a Newtonian potential term for the gravitational field. And this is the thing I call the Schrödinger-Newton equation. I think other people have worked with these things in other contexts and give them other names, but I'm going to call it the Schrödinger-Newton approximation to the scheme that I'm talking about here. So for one question that's of interest, suppose you have just a single-point particle. Do you get nonsense for a single-point particle? Remember for a nucleon I said, I got 10 to the 7th years but that was thinking of it as a solid sphere, uniform sphere but if you think of it as a point particle but where you have to look at it as a stationary solution of the Schrodinger-Newton equation, where it's got the Schrodinger equation for the particle, the point particle, plus a term which is the Newtonian gravitational potential, and you have a coupled non-linear system of equations which you then have to see whether they have nice solutions or not so my colleagues Aline Moroz and Paul Todd looked at this very seriously

52:30 and found that there were families of very asymmetrical solutions and one only one which is the one you should take sort of a Gaussian-like thing which has one peak and then others with other nodes but these ones are probably unstable so you should probably take the main one. So it looks as though it makes good sense for a single particle. Nobody yet has done it for well, even for two particles let alone a crystal you could do this try the hydrogen atom or something but the question would be do you get sensible answers does it more or less say what I say what I'm suggesting is that you just solve the Schrodinger equation forgetting about the Newtonian potential term and you just use the Newtonian potential term more or less to make the center of mass localize itself that's more or less it that's the idea well I don't know to say a great deal or more about this. There are some scaling properties that these things have which mean that if you know what solution is for one single particle then you can just scale up and down. This is giving you the scalings on this piece here. So basically just one solution for a point particle. And for many particles you'd have to solve these coupled systems here. Okay, this is the what I call the Schrodinger-Newton approximation. Of course, one should really do it in proper GR. There's an additional advantage in doing the Newtonian approximation, of course, and that is you get around the major problems, I suppose, related to what Chris Ayshin was saying. Thank you. What Chris Ayshin was saying about Perch and Specker and people like that, and theorem and those things which are supposed to make you think that you can't take quantum mechanics realistically. What they do say is that you can't take quantum mechanics as a local theory. It's got to be non-local. And certainly that's very much a feature of the things I've been talking about. For example, when I said the environment is entangled with the system, if production takes place in the environment, it brings the system with it. So the whole system has to be considered as a holistic thing, which we know we have to do in quantum mechanics anyway. The sort of most famous example of a holistic system is the EPR thing, which I talked about before.

55:00 Here we have two particles. So in this thing, they're photons. They're two photons going two opposite directions. And the problem is, of course, if you make the picture here, suppose you think of the state reduction as realistically happening. It depends on whose frame of reference you look at. If it's A's frame of reference, then the measurement takes place here. the state is reduced before this one does the measurement. If you take B's frame of reference, the measurement takes place here, and the state is reduced before A makes the measurement. You get the same answers, so most people wouldn't worry, but if you take reduction as being something real, which actually happens out in the real world, there's a problem if you want to try and make it consistent with the principles of general relativity, even with special relativity, I should say. Now, except for all that, some people, I think John Bell, would have said, let's give up the principle of relativity. Now, I've been brought up as a relativist. I don't like that point of view. And I'm going to suggest something else to you, which has also been put forward by other people. I'm going to coin this word cranglement here. Cranglement means what other people might call quantum information. But quantum information is a bad word, it seems to me, because it's got the word information in it. and then people worry about what I'm about to say here well this is the famous quantum teleportation experiment well real experiment now where we have Alice and Bob who each have a sealed box with a particle in it one member of an EPR pair and Alice is to transmit to Bob by a classical signal an unknown quantum state so here we suppose they're all spin-half particles this unknown quantum state does is to make a measurement on putting this together with her particle in her box here, make a measurement on the two of them. It's a four-dimensional Hilbert space, and you make these four different measurements, which distinguish between what I call these bell states, and whichever one it is, it's just two bits of information, four outcomes. You send that with a classical signal to Bob, and Bob, on receiving that, takes his box and does one of these four different rotations, possibly the null rotation, and it produces the initial state. So this is where we're teleporting the state from Alice to Bob.

57:30 But the puzzle is, if you look at this space-time diagram, you see this state here. Remember, a quantum state is a point on the Riemann sphere. And from a mathematical sense point of view, if I can use information in a mathematical sense, the information is a point on the Riemann sphere. And that point on the Riemann sphere has propagated itself out to Bob. Yet only two bits of classical information have gone from here to here. So what this is telling you, you just look at the picture, there's no other way, there's no other link apart from this, which goes back in time and up here. So it seems to me that you have to accept that quantum information, or as I said, what I'm calling quanglement, is perfectly well allowed to go backwards in time as well as forwards in time, which is fine if you don't think of it as information. You can't use quanglement to send a signal. Equivalent, sure, it goes backwards, and you can zigzag it backwards and forwards in time if you like. There is a suggestion of that sort and so on. Fine. And that's the sort of thing which is happening here. The way to understand the situation here is to think of it as the equivalent is allowed to go back here. It's not really the reduction in either of these. You just have to change your perspective and look at it from this point of view. I think that's all I want to say, so thank you very much. Thank you.