Why We Need to Gravitise Quantum Mechanics

0:00 Thank you. Okay, so welcome everybody to this first Petra Telemann lecture by Professor Pembrose. Professor Pembrose is an emeritus Roosevelt professor at the Mathematical Institute of Oxford, University of Oxford. he is perhaps the most influential figure in the field of general relativity most of the relevant results during the 60s, 70s and 80s that led to this period of time the golden age of general relativity are related or directly related or have to do with the contributions of Roger Penrose. Some examples of that are the singularity theorems. Roger Penrose invented mathematical tools that were necessary to prove these theorems that show that gravitational collapse generically leads to the development of singularities. other results related to black holes are the Penrose mechanism where he showed how one can extract energy from rotating black holes the cosmic censorship conjecture that gives great physical relevance to black holes which are by now supported by a huge amount the Newman-Penrose formalism and the by curvature hypothesis which is a way of understanding the arrow of time in our universe and the second principle of thermodynamics on the mathematical Penrose discovered Penrose stylings which have been observed

2:30 in certain crystal structures in nature the development of the spin networks which are of loop-quantum gravity, which is one of the fields, important fields here in Marseille. Generalizations of the idea of spin networks came to the theory of twisters, which allows to try to formulate the theory of general relativity in terms of a fundamental structure and perhaps go beyond to quantum theory of gravity. Twisters are used in loop-quantum string theory, and recently have found applications in high energy particle physics. So the talk today, I believe, is on the subject of related to quantum gravity. Penrose is a proponent of an unorthodox view on the way one should quantize gravity, in which one should not simply apply the usual recipes of quantization to the gravitational field, but rather use a subtle interplay between geometry and the geometry of the space type and the quantum. We are greatly honored by your visit. Let us welcome Dr. Kermos. Thank you very much for that introduction. It's a great pleasure for me to be here in Marseille and I hope I can explain various things which I'd like to say I apologize for using this old-fashioned technology I had to change from using blackboards to this and one change in a lifetime is I think enough anyway, here is I believe the title of the thought why we need to gravitize quantum mechanics I'm using the term gravitize, you see, as a sort of opposite to quantize. So quantizing gravity is accepted as one of the things one ought to try to do. And I'm saying that we maybe should also think about the reverse process of gravitizing quantum mechanics. And the idea is basically... Let's think of the way to get rid of these things appropriately.

5:00 the question is to bring together the two major revolutions of 20th century physics which were general relativity and quantum mechanics and they're both magnificent theories which have changed our view of the world general relativity telling us that space and time have to be regarded as curved in some mysterious way and this explains the phenomenon of gravity has completely changed the way in which we look at matter and reality in many ways. The question is, should we just? Well, I put quotes around just because it's not a thing that is trivial. In fact, no one really has, in an accepted way, succeeded in quantizing general relativity. That's to say, applying the rules of quantum mechanics to general relativity. So changing general relativity in accordance with the procedures of quantum mechanics. That's what we usually mean by quantum gravity. Or should we seek a more even-handed marriage, we'd give on both sides. So not only would our combination change general relativity, which is accepted, but it would change quantum mechanics, and that's not accepted. So I'm trying to argue not that we should leave general relativity as a classical theory. I think there will have to be changes to general relativity, stressing is that there should also be changes to quantum mechanics in accordance with some of the principles of general relativity. So the common view, I mean, I'm just making one perhaps. One of the reasons that people think of general relativity as secondary in quantum mechanics is primary. I don't know, they don't say this explicitly, but I think it's something like this. That quantum mechanics, roughly speaking, deals with small things, and general relativity deals with big things and the feeling is somehow that big things are made up of small things and so therefore the theory of the small things is more fundamental. And I think there is this feeling, although not said explicitly, that okay, we're made up of atoms and atoms are made up of molecules and atoms are made up of molecules and atoms are made up of particles and so on. And so you go down and down and down and then you see quantum mechanics rules and therefore when you go back up it must be quantum mechanics all the way up. But I'm trying to argue that

7:30 this is not necessarily the case, that there is some respects in which general relativity must be regarded as more fundamental. I should say both are unrefuted by current observations. People often say that quantum mechanics, oh, it's a very strange theory, but there are no observational facts which contradict the was in quantum mechanics. This is also true of general relativity. Okay, it's a strange theory, but there are, again, no observational facts which contradict the theory. And for this, I should stress that the theory as introduced by Einstein, originally, he had to modify... Well, he didn't have to, because in those days, the modification that Einstein introduced in 1917, Well, the theory was produced in 1915 and 1916, and then he decided in 1917 to put in a thing called the cosmological constant. He put it in for the wrong reason, because he believed that he wanted a universe that was unchanging, a static universe, and it shortly afterwards became evident that the universe was expanding. And so when Einstein realized this, he is alleged to have said that introducing his was his greatest mistake. However, as we know from observations towards the end of the 20th century, in 1998, two groups, and they both later won the Nobel Prize for this, realized that the universe is accelerating its expansion, and this was all regarding a great mysterious thing, this dark energy, this mysterious dark energy. Well, if you read any cosmology books, you'll see the cosmological constant is there. Whether it was a mistake or not, according to him, it turned out to be correct, or at least it agrees with the observations. So when I say general relativity, I mean general relativity together with the cosmological constant, which now seems to be observationally confirmed, even though he regarded it as a mistake when he realized the universe was expanding and he could have predicted that if he hadn't introduced this constant. both are refuted by current observations and that as I say means including GR includes the cosmological constant in a certain sense there's even

10:00 more precision in general relativity than in quantum mechanics clocks are now so precise that the timing of general relativity events and this includes the pulse of the neutron stars going around each other and so on binary pulsars and things like this which are so incredibly precisely tracked and confirmed the theory of general relativity to a precision which is even greater than the precision we see in quantum mechanics or quantum fuel theory. A little bit greater. Well, when a fuel modus of magnitude is greater. But quantum mechanics, of course, has many, many more effects which are confirmed. So, okay, general relativity has a bit more precision. Quantum mechanics has hugely many more effects which are explained by the theory. And I suppose that's one reason why people are more likely to believe quantum mechanics than general relativity if there is a conflict between the two. But I'm going to try and argue that that need not be the case. Okay, so that's the general point of view. Now, I want to start by talking about quantum theory, and I imagine that most people here really well know what quantum theory is, but just in case there are one or two people who are not familiar with it, I just want to give you a quick rundown, and the rundown is basically indicated in these two idealized experiments, where here we have a laser, say, which emits light, and we can cut down the intensity so it's sort of one photon at a time. Now, when these photons encounter this thing here, which is called a beam splitter, sometimes referred to as a half-silver mirror, so half the light goes this way, half the light it's reflected, and you have detectors here and here, and what you find is that with this situation, that each individual photon is either detected here or detected here, never both, never neither. So you see it's always one or the other exclusively in an idealized experiment. Of course, if it wasn't ideal, you'd lose them occasionally or something, but let's say it's an idealized experiment, and this means that it's either this detector detector. And that's the particle-like behavior. However, if you put ordinary mirrors here and another beam splitter, or half-silver mirror as you might call it, would in fact

12:30 be made that way, but never mind. So we have the photons, could take this route, could take this route, or that route, or that route, and you might think that these two detectors would be equally likely to detect the photon, but what you find, and let's suppose that what you would find is that it's always this detector that receives the photon and the particle explanation simply doesn't work for that because it would have to do all the possible things but what you find is that these two roots somehow mysteriously cancel each other out and if it goes that is to this root cancels out with that root and so that never that detector is never received whereas this one always receives the photon And this is explained by thinking of as little waves, so the waves going this way, and their waves add up this way, and if they go this way, they cancel out. However, these explanations are in contradiction with each other, that you can't imagine this one done by little waves. You see, suppose this was waves, then the waves could sometimes go this way, some this this way. And if they were little waves, then this detector would half the time see it, This one would half the time see it. But this means that a quarter of the time neither of them would see it, a quarter of the time both would see it, and only a quarter of, half the time would it be one or the other. So that wave explanation doesn't work for this, and the particle explanation doesn't work for this. So what do you do? Well, you have a very peculiar rule in quantum mechanics, and you say that in a certain sense, between the emission and the detection, the alternative things which might happen simultaneously happen. So alternatively, A, which is A, it takes that route, or B, it takes this route, somehow both happen at once. So you can have the particle in two places at once. Not only that, but there is a sort of factor telling you how much of it goes one way, and how much of it goes the other way. You might think that's a probability of going one way, the probability of going the other way. No, that doesn't work. These have to be complex numbers. They have to be numbers which involve the square root of minus 1. Very mysterious, of course, but that's the formalism you have to adopt to make it work. That's square root of minus 1. You can plot that on the plane with the square roots of the imaginary unit i,

15:00 this going this way, and multiples of that, and the real unit's going this way, and every complex number is a point on the plane. And then you have the rule, is that when you make a measurement, this is called the Born rule, when you make a measurement, This superposition shows your measurement just to look to see which of those two alternatives takes place. Then you look at these numbers here. They're what are called probability amplitudes. They're not probabilities. They're complex numbers. But what you do is you take the squared modulus of each. In other words, you take the distance from the origin in this diagram, and you square that, and those give you the relative probabilities of one or the other. So that's sort of, in a nutshell, what you do in quantum mechanics. But I want to emphasize a particular property of these superpositions, which is very important to the way quantum mechanics operates. It's fundamental to the Schrodinger equation, the Schrodinger equation I'm using the letter U for. Well, Schrodinger's name doesn't begin with the U, but it's U stands for unitary, which is basically what we're concerned with here. You see, there are actually two procedures in quantum mechanics, to emphasize that these two procedures are central to quantum mechanics, but they are in contradiction with each other. So that's very mysterious. Quantum mechanics has this curious feature that it consists of two rules which are in contradiction with each other. Actually, I'm slightly puzzled by something here. I thought I had a transparency which I didn't show you, which is puzzling me. Yeah, I see. Okay, let me talk about that, because... Let me finish talking about this slide, but I realize I did things in the wrong order. I'll come to that in a minute. What are these two rules here? Well, the unitary rule is the Schrodinger equation. That tells us the one feature I want to concentrate on is what's called linearity, and I'll come back to that in a minute. But what it says is that if alternative A is one thing that might happen, and that will satisfy this equation, alternative B is another thing that might happen, and what happens in these superpositions is it just chugs along with each one following the same equation,

17:30 and these numbers remain constant. So whatever that evolution is, if superposed with this evolution, those two things will evolve together, these numbers remain constant. And I'll say a little bit more about that shortly. But when you make the measurement, that's the other procedure, that you do something completely different, and suddenly you say these are alternatives that your measurement is distinguishing between, and that these things, if you square them, you take the squared modulus, which is the square of the distance from the origin, then they do give you probabilities. They become probabilities when you make a measurement. But the conflict between these two things things I want to stress. And now let me come back to the transparency which for some reason didn't discuss I seem to be badly handling this because I put it down. Here we are, okay These are some reasons to question whether quantum mechanics can be universally true particularly in a gravitational context and one of these is this I'm referring to measurement as the measurement paradox. I mean, measurement paradox, some call it the measurement problem. I'm calling it the paradox, that's a terminology that was introduced by a distinguished physicist whose name just slipped me out of my head, but never mind, I'll come back to that. I'm going to call it the measurement paradox because it is actually, these two procedures are in contradiction. the R procedure and the U procedure really they fit together very nicely but they're strictly speaking contradict each other so there's something puzzling about that so this is a paradox Tony Leggett was the man I was referring to you see it's usually called the measurement problem but I think it's more serious than that it really is a paradox because it's a contradiction between the two main principles you use another thing is the black hole information paradox I won't talk about this here but I will say that when you talk about black holes and this is where gravitation is really important it's an absolutely crucial part of gravitation theory which gives rise to these curious things called black holes and there is this thing called the information paradox

20:00 that people argue about endlessly because it contradicts the U part of quantum mechanics. So this is the Schrodinger equation part of quantum mechanics, and it disagrees with that. And so people don't like that. They say, well, oh, no, no, no, you mustn't get rid of U. It's got to be true all at levels. And then you run into this thing called an information paradox. And then you run into these things called firewalls. I'm not going to talk about them, but I just say that some people say, oh, well, black holes can't be there because if you take the unitary evolution at all levels, then you conclude that there must be these things which if you tried to approach a black hole, you'd run into one of these firewalls and so on. And so this is one of these reasons. You run into trouble if you take quantum mechanics seriously, completely rigorously seriously, at the level of gravitational phenomena. now there is a clash of basic principles some of these I will talk about there's this thing called the principle of general covariance which is part of the theory of general relativity which roughly speaking tells you that you can use any of your coordinates you like and the theory still works I won't go into there much but I'll talk a little bit about that later on the principle of equivalence which is that is equivalent to an acceleration, which is now familiar to us that astronauts as they go around the Earth don't feel any gravitational field even though the Earth is just sitting there. And as far as they're concerned, the gravitational field is just the same as an acceleration. Well, you notice this if you're in a train and the train is going around in a curve and everything seems all at an angle. Why is that? Well, it's not really as an angle as you like, but it's because the acceleration of the train and the gravitational field that you can't tell one from the other. Or in a plane, when it's going around, turning a corner, and you see the Earth is all tipped up. So it seems that it's because the acceleration in the plane just feels like a gravitational field. And that's the principle of equivalence, which is central to general relativity. And that these principles of general relativity are in sort of contradiction with the superposition principle of quantum mechanics. And this is the issue here, the superposition principle of quantum mechanics

22:30 is the fact that you make these superpositions universally part of quantum theory, and they have a certain contradiction with these principles of general relativity, which I will address later on. Secondly, or thirdly, or whichever I've got to here, is the singularities which we just mentioned earlier, in general relativity the black hole singularities and the big bang singularity and all that If these are to be resolved by quantum mechanical procedures, why do they have this extraordinary asymmetry in time, which is something we do feature? This is something which I'll talk all about in the lecture I'm giving on Thursday. It will be quite an important central part of the talk, like I've done. I won't say anything significant about it here, but it does indicate that there's something funny going on when you talk about quantum mechanics as applied to the universe as a whole. So there are issues here which do suggest that there is some limits to the rules of quantum mechanics. But as I said, some of those I will address, but I won't talk about all of them. Okay, well let's say a little bit more about the linearity of quantum mechanics. I will refer to this in the following way. Let's imagine that we have a laser which emits a photon, and this photon hits the brown thing, I'm not saying what it is, something or other, and a whole lot of stuff comes up. In detail, I don't care what it is, but that's what might happen. On the other hand, you might have a mirror, which you impose between the brown thing and the laser here, and the photon goes another way and hits a green thing, and a whole lot of stuff comes out, different stuff. Now, suppose that was not a mirror, but a beam splitter. then what the linear superposition rule will say is that this alternative and the other alternative will happen simultaneously and therefore whatever the green stuff is

25:00 and whatever the brown stuff is they will both happen together as part of your state of the world so the state of the world according to the unitary evolution or according to the Schrodinger equation will be that these two things they will be in superposition ok, now Schrodinger of course who started all this introducing his equation considered a particular situation not quite in the form I'm giving you here but this is referred to as the Schrodinger cat this is not quite his version but it's basically the idea and here we have this slightly inhumane experiment If you have to bear in mind, this is a thought experiment. So Schrodinger, who was a humane person, would never actually suggest him doing such an experiment. But it was something he considered as a hypothetical possibility. Here this photon goes along, there's the detector, and it kills the poor cat. Okay. Now, of course, that's not going to be the whole story, because you can interpose with the mirror, and because of the quantum linearity that we've been talking about, if that happened to be a beam splitter instead of a mirror, then you would have to have the superposition of the two alternatives, the green and the brown, together, which in this case would mean a dead cat and a live cat simultaneously. So Schrodinger was saying, well, if you believe my equation, my equation, I mean his equation, of course, then you could easily set up an experiment in which there was a cat which was alive and dead at the same time. And he was more or less saying, well, look, that's absurd. You never see cats which are alive and dead at the same time. There must be something else to the story. This can't be the whole story. So he worried about this. Sometimes he worried about it openly and sometimes in private. People often say, however, well, look, you could do that if you like, but you've forgotten various things. You've forgotten the example. For example, there is the environment, which I've indicated here with a lot of dots, which is the atmosphere. You've forgotten that an observer might come along and look at the cat, and you've forgotten that the observer might have some perception of the cat. And then what happens? Well, I haven't, of course, forgotten that, because if I had, I wouldn't be showing you these consequences.

27:30 Let's put the mirror in, and then, of course, here's the other thing that might happen, environment is in a slightly different place. You may not remember where all the dots were in the previous one, but there are slightly different places. And the cat is alive now, and here we have an observer looking at it, and the mental image that the observer has is indicated as an alive cat. You might say, well, how do we know how to represent mental images quantum mechanically? Well, you need to worry about that because you look at the expression on the person's face and you see the smile there, whereas in the other case, observer have a rather unhappy expression. But of course you then say, well, what happens if we put the beam splitter in there? Okay, yeah, there's the environment. You have a superposition of these two slightly different environments. You have an observer looking at the cat and a superposition of images and therefore a superposition of expressions on the face of the observer. Some people regard this as a solution to the problem somehow. There are certain, it's an interpretation is referred to as the many-worlds interpretation, which suggests that somehow this being looking at the cat has two instances, one in one's world and another in another world and so on. That's in fact where you're driven. If you don't change quantum mechanics, you are more or less driven to that view that there are two worlds driven there, but on the other hand, it's not a happy place to be, because not just do you have a multitude of different worlds all simultaneously existing but you also have problems of how to explain the probabilities and so on which is what you really observe and the Born rule which I mentioned where does that come from so there are lots of questions which are left unanswered by this what really happens is that you the cat is either alive or dead and somebody comes along and sees either a live cat or a dead cat and so on and how do you accommodate that within the framework of standard quantum mechanics. Well, the usual view is, well, you've got to do it somehow. And quantum mechanics is right, and so therefore you have to come to terms with this in one way or the other. Maybe it's many worlds, maybe it's some way, because the interpretation of all the environment gives you... Well, I won't go into them all. Because my view is that none of those is the answer. The answer is, well, you see here, I'm not going to say Schrodinger's cap anymore,

30:00 Schrodinger's love. You see, bringing the cat in is slightly confusing the issue, because you might worry about what the cat thinks. And the cat maybe has its own view of the things, and how can it imagine itself to be alive and dead at the same time, or does it inhabit one world and the other world at the same time, and so on. But I'm going to say that it's unreasonable. I think Schrodinger was saying the same thing, but he was a little bit cautious, more cautious than I'm being about what he was saying, I think he was saying, we really need a new theory. That the theory as it exists is incomplete or even wrong. See, Einstein was certainly on the side of thinking that there's something more that has to be understood, that the theory is incomplete. Schrodinger had this view, and even Dirac, who was the person who really formulated at first a whole framework that everybody uses in quantum mechanics these days, and he was skeptical that the quantum mechanical formalism that he himself had basically formalized, along with von Neumann and others, he was saying, this is not the complete answer, there must be more to it. So, on the other hand, there were people like Heisenberg and Bohr who tried to say, well, well, the theory must be right, and we've got to come to terms with it somewhere. So I'm trying to say that the theory isn't right, and there is a level at which you start to notice that it's not right. Now, my point of view, there are many points of view, you find various different theories where people suggest modifications of quantum mechanics of one form or another. One of the most interesting ones was by Simitalians, Girardi, Rimini, and Weber, introduced a modified idea which made sort of sense. It's not necessarily a correct theory. I'm not sure they believe it is a correct theory. But nevertheless, it shows how you can modify quantum mechanics to give you things which would make sense at the level of the measurement paradox and would resolve it within that framework. Now, this is a slightly different version, what Girardi, Remini, and Wever introduced. But I'm saying that it's gravitation

32:30 which is the crucial thing. So Schrodinger's lump is just some lump of material which, if the photon goes this way, it gets moved into this location. If it goes the other way, it stays put in the original location. And that, according to the Schrodinger equation or the unitary evolution, we will have a superposition of those two alternatives. But I'm saying that if those lumps are big enough in some sense that superposition will exist but only for a limited period of time. And if this lump was anything sizable that you could see that length of time would be a tiny fraction of a second. So it would look as though it was one or the other. However, if it was just a neutron or something like that it's sufficiently un-massive that it could exist in a superposition for a long time. Now, how long is that time? Well, I can give you the proposal here. I should say that the proposal of this type was introduced by Diyoshi before I started thinking about these things, when in a serious way like this, and the proposal I'm saying gives an answer which is the same as Diyoshi's, although I had different motivations behind it. I'm calling this gravitational OR. OR stands for objective reduction. The reduction is the superposition becoming one thing or the other. And I'm saying that it really happens. It really does become one thing or the other in a time scale that one could compute. So it's gravitational. So to work out the time scale, you need to bring in gravity. Now what is the rule? the rule is that well you see there is a thing EG which you calculate from the mass distributions in these things here and this EG is to be interpreted as a sort of uncertainty in the energy of the system as a whole this thing H cross or H bar is the Planck's constant divided by 2 pi Dirac's version of Planck's constant and EG well, what is it? It's the gravitational self-energy of the difference between the two mass distributions. So that's quite well defined

35:00 at least in a Newtonian type of scheme we say, okay, if the lump was over here, it has a certain mass distribution if the lump was over here, it has another mass distribution. What I'm going to do is say, take that mass distribution, subtract from it this mass distribution that's a bit of a funny thing to do physically but mathematically you can do that I say it's positive density here and it's negative density over there so I subtract one from the other and then I get a resulting distribution of mass negative and positive in some places negative in some, positive in others and I work out what's called the gravitational self-energy of that difference of that mass distribution and that is EG It's, roughly speaking, the energy of displacement of one lump in the gravitational field of the other. So that's to say, if I want to work it out, I would imagine two lumps on top of each other. There's only one lump, really, but just imagine two on top of each other. And then I pull one apart from the other into this super-closed location, and I work out how much energy that would cost me if I just consider the gravitational attraction. So I don't worry about any other form of attraction, just gravity, how much energy would that cost me to pull them apart. And that's what EG would be, so long as it's a rigid displacement. If it's not a rigid displacement, you have to do the calculation the other way, but this is more or less it. Okay. I'm going to give an indication of why I say that, but it's at least a well-defined calculation, provided these lumps were in each state individually would be stationary. So I'm supposing that the two states either here or here would be, if left on its own, would just stay there. So each one would be on its own stationary. But if I consider the superposition then I'm saying it has a certain lifetime. And that lifetime I can calculate and it will go to one or the other in that lifetime. So that's the idea. shortly some of the reasons for suggesting that but for the moment I put it another way, which is perhaps quite useful here we think of the lump again, moved into a superposition of those two by the beam split fojan, it either goes this way or that way and so what you have to consider is that

37:30 it's a superposition of the two and so the lump's in the superposition of the two but it will become one or the other in a certain time, well I've got two outcomes to this story here you see, either it's the gravitational self-energy of the difference, which is what I said before or the easier way to think about it is to say it is the energy of the cost to displace one instance of the lump in the gravitational field of the other displacement, that would be the answer. Now watch this picture here. This picture is an attempt at a space-time picture of what's going on. Here we have time going this way, here we have space going this way, and the little dip here is just the curvature of space that would come about through Einstein's theory. Einstein's theory tells you that if you have a mass distribution that would curve space, And I'm trying to indicate that curvature by this thing. The space is only one dimension, I'm afraid, so you have to imagine that that's all there is to it. All the other dimensions are squashed into that line there. As time evolves, these two space-times separate from each other in the sense that it's a superposition of those two different geometries. But the idea is that this superposition of two different geometries is something which has a lifetime the lifetime of that well I'll come back and have you have other pictures of that in a moment but let's try and see what the reason for suggesting a lifetime of the kind I've just given you would be here we'll be getting a little bit more technical but let's do it anyway I want to consider the superposition of a pair of lumps. But let's say they're both sitting on the ground, and that the energy of each is the same, it's just that it's located in a slightly different position. Now, how do you say that a lump is in a stationary state, according to general activity, when you say there's a displacement in time, which doesn't change the situation. So if I go back to my previous picture,

40:00 to say it's stationary, that's a, take the original location here, say, to say it's stationary means that you could slide the space-time up along the time direction, and it's the same, looks the same. So it's got a symmetry in that time direction. That's what stationary means. And as you separate them, of course, they can't be stationary, but then after a while they may settle down, and each alternative would be stationary. suppose that's the case. So we suppose that each of the alternatives is stationary. And the technical way of saying that is that in space-time you've got a thing called a killing vector. That just means that you've got a vector field which points in the time direction, and things don't change with respect to that. So this is a little bit technical, but this is the way you write this thing. You say that there's time displacement this is the Schrodinger equation in this Don't worry about the details if you're not familiar with quantum mechanics. But according to quantum mechanics and the linearity, if each one is individually stationary, then the superposition will also be stationary. So that's complete degeneracy, that is to say, all the different superpositions will be just as stationary as each will be. But now I want to bring in the gravitational field of the lungs. How are we supposed to consider Let's try. I've got a space-time picture of a lump, and considering it being stationary. And this thing down here is the thing I called T before, saying that the derivative with respect to time is unchanging. Now I'm going to take this stationary situation, and I'm going to... here we have it superposed and then I'm going to say well I consider a superposition of two locations what does it mean to say stationary well you've got these vector fields so these vector fields if you slide it along those vector fields the space time won't change if I slide it along the other one the space time won't change but then when I have a superposition of the two space times it's a little bit obscure what that means because the very notion of stationary is different in each of the space-times.

42:30 And if I try to, say, I have a notion of what I mean by a killing vector field or a stationarity notion for the superposition, I'm confused, I don't know what I mean by it. And this is the trouble, because general relativity tells you you've got to have a space-time in already before you can tell what stationary means. And if I have it in another place, well, I somehow should be able to superpose those two space-times. them together, well, let me just, so I'm going to do this, it's too hard to do it in proper general relativity, so what I'm going to do is to consider that the speed of light has gone to infinity. So I'm taking a limit, sort of what you could call a Newtonian limit or a Galilean limit, which means take the speed of light as being infinite, and then things become easier. But these operators here become differentiation, partial differentiation with respect to time. So I have these two operators, and when I slide this along, well, you see the times don't change, so you might think these things don't change. You might think that, but you'd be completely wrong because of what my colleague, Nick Woodhouse, used to say this is the second fundamental confusion of calculus. That's to say, if all your variables change except the t, then d by dt is the one that changes, you see, because of all the chain rules, you've got all these extra terms. So if you know what I'm talking about, yeah, that's fine. It says that even though the times are the same, the d by dt's are different, because they depend on all the other coordinates. Okay, so, anyway, I'm trying to make here is that these notions of stationarity are not the same. They don't mean the same thing anymore. And how do you do it? Well, I don't know how you do it. But what I'm going to try and do is to say, well, we know we're making a mistake if we identify these two spacetimes. Because the principle of general covariance that I mentioned earlier, that is to say that the coordinates aren't important. It's the spacetimes that are important. And you don't know, if you've got two completely different space-times, you don't know which point over here is really the same as the point over here. And that's all the coordinate thing. And so that's why you can't say what the killing vector means on this picture.

45:00 They're two different sets of vectors. And what does stationary mean in this picture? Stationary in this picture means something different from over here. So I'm making a mistake. And the mistake is somehow an error because these errors aren't the same. And so I try to estimate in what way are those errors different. Well, it's really not quite what I'm saying there. Let me say a little bit more accurately what I should be saying. You see, what I should be saying, these lines here are not the killing vector so much, but those are the free-fall accelerations. So general relativity is saying, according to the principle of equivalence, but I'll come to it more seriously in a minute. It's saying that falling freely is the same as what we see. The acceleration you feel in an airplane or a car or something, or in an elevator or lift, is equivalent to a gravitational field. So these lines here represent what free fall would be. See, if you have a... As time progresses, that's going up in the picture, something drops towards this lump here, it would follow a path like that. And if I then move the lumps, then free-fall will be slightly different. So whereas they're the same, if they're in the same position, when I move them to different positions, free-fall will be slightly different. And so what I do to see what the error in this is, is I take these different free-falls and I measure how badly off they are as a sense of the error made in making this identification. That's a little bit vague, and I'm going to do something which is more precise in a minute. But the idea is, okay, let's say that the error in making this connection, this identification, is by identifying these geometries. There's an error there, and you can estimate the size of that error. And that's really what I'm doing here. So I say, I integrate the, these f's represent these acceleration fields, and I take the difference between the square of them and integrate them, and then I convert that into integration by parts, and so on. I won't get into the details of this. And then after the end, I get this. What is the measure of this error? It's the gravitational soft energy of the difference between those two mass distributions. So this is the calculation you do,

47:30 which is a fairly straightforward one, but let me not spell that out here. That is the rationale for this expression that I had before. of the error in making the identification between these two different geometries. Okay. Now, sometimes people say, well, okay, that's fine, but gravity is such a tiny effect that how is that going to have any influence on what you do here? Well, I've just drawn the same picture again, really. here we have these space times initially when the lump is just in one location it's represented here but then as I move one instance of the lump away from the other one I have two different space times which are supposed to be in superposition then there's a reduction takes place one of them dies off and the other one is the continuation of what actually happens in the world so that is the picture here, where you have a superposition of two different incompatible geometries. And you might say, well, surely that's really tiny. Indeed, it is tiny. You see, people often say, well, quantum gravity effects must be ridiculously small and totally ignorable in a situation like this. And the sort of reason people say, well, the fundamental distances that you get in combining quantum mechanical and general relativity, these things called the Planck distance and the Planck time. The Planck distance is 10 to the minus 35 meters, roughly speaking, which is about 20 orders of magnitude smaller than the sorts of scales you get in particle physics. So you're looking at something which is 20 powers of 10, smaller than the normal sorts of sizes you get with particles. It's smaller than you can go a little bit further down depending on what energies you're talking about. But Planck's time is a ridiculously tiny fraction of a second, 10 to the power of minus 43 of a second. And so people tend to say, well, these things are so small, that why should we have any relevance to ordinary scale phenomena? But the thing is that when you look at this formula,

50:00 you see indeed, Planck's constant is really tiny and that's this h cross thing here but the eg is also really tiny and you've got a ratio of two different tiny things and this ratio of two different tiny things may not be small at all so it really depends on the details you might have something from which this time to pick one or the other is quite a reasonable thing in ordinary scales of time I'll say that these timescales can be perfectly reasonable timescales that one might imagine measuring physically. Now, let me, I think I've got the same, basically the same picture here, but let me just leave again. So this is the superposition of the two spacetimes, and there is a region where they differ. And the question is, how big is that region? well that region in terms of these sort of Planck scale units which I've just given you those tiny things is on the scheme it's about one Planck scale unit so I'm saying that ok these space times differ only in a very very tiny amount they only to make that Planck time scale length of time That can be a very tiny fraction of a second, too. So, well, as I say, you have to look at the details. But the formula which I just gave you can be expressed in a different way. In fact, this was the first way I came across it. It was not the way I just described. I was thinking about when you take space-times and you try to see the difference between them spatially and the difference between them temporally, to be roughly of the order of one unit in these Planck scales, that gives you the length of time that the superposition will exist. So from sort of fundamental aspects of quantum mechanics and gravity brought together, it's a reasonable expression. It's telling you how long can that tiny separation between the space-times, which is indeed remarkably tiny,

52:30 how long can that actually survive? well, the Planck time is a remarkably small time. So the smaller the separation is, initially the longer they can last for, and if the separation is quite large, then it will be a very short time scale. Now, I'll come back to those things. Later on, I'll talk about the experiments. But you can come about the formula I gave you by just thinking about geometry, separations of geometries from each other in terms of Planck units. does give you a similar expression. Okay. Now let me give you what I regard as the most rigorous definition, the most rigorous derivation of the formula which I've given you. this is the following. It is based on the principle of equivalence. I talked about that before, and here we have pictures doing it. Here is Galileo, if you like, and whether he actually did this, of course, is disputed, but he certainly imagined that you might drop a large rock and a small rock from the Leaning Tower of Pisa, and the thing is that they would drop, if you could ignore air resistance, they would simply drop at the same rate and reach the ground at the same time, even though one is much more massive than the other. And if you think of that in another way, if you imagine you were a little insect sitting on one of the rocks looking at the other one, then the other rock would just hover as though there were no gravitational familiar thing now with space travel, so you imagine that they have a rather futuristic space station, and they seem to hover there, as though there were no gravitational field, despite the fact that the Earth is just sitting there, and that's because, of course, they're falling freely, they each fall freely together, and that is the principle of equivalence, which is the foundation stone of Einstein's general relativity. So this is a foundational principle of general relativity. Now, is that foundational principle of general relativity consistent with the rules of quantum mechanics? Well, that's the question I want to talk about here. So let's think of a simple experiment where you have maybe something done on the tabletop in a lab, and you want to take into consideration the Earth's gravitational field. So you might say, well, one of the forces we are going to consider in our

55:00 experiment is the Earth's gravitational field. Now, there are two ways you could do this, in standard quantum mechanics. Well, there's the standard way that a good quantum physicist would do, which is what I call the Newtonian way, which is to put a term in the Hamiltonian in for the gravitational field. So you just consider the gravitational field to be just like another force. Do it the same way you would treat other forces. That's one way. That's the Newtonian way. The Einsteinian way is to say, no, no, there is no gravitational field, it's really an acceleration, I consider another frame of reference, which is dropping freely. So the purple ones are the Newtonian, no, the green one is the Newtonian one, that is where the gravitational field is treated as just another force. The purple one is the Einsteinian one, where it isn't a gravitational field, but you're looking at an accelerated train. And then you just do your quantum mechanics, you've got a wave function in one system or a wave function in the other system, and then you say, well, do I get the same answer? Well, I have to transform back from the accelerating frame to the other frame, and I do it, and if you check all this and do it yourself, if you want to, I'm not doing the details here, but you can just work it all out. And what you find is that the wave function, is the thing Jodinger will use for his equation, is you have a purple one, which is the one in the Einsteinian frame, that's the Einsteinian wave function, and you've got the Newtonian wave function, which is considered in the gravitational field just another force, and you find that the two are in a sense equivalent because they differ only by a phase factor. Now, the rules in quantum mechanics is if you just have a number here which is a complex number which is of unit modulus, the unit circle, the unit distance from the origin, then these things are equivalent. So that's the sort of conventional view. In fact, there were experiments done by Colella, Oberhouser, and Werner a long time ago in which they actually did experiments to see whether the principle of equivalence was satisfied in a quantum system. And they found, yes, it was, and they also considered something a bit like this. that showed that the wave functions were equivalent. However, if you look carefully at this term here,

57:30 you see that there is a T cubed. T is the time. It's the same in both of these coordinate systems here. But you've got a T cubed in this factor here. Now, what does that mean? Well, it means, well, first of all, if you take a general system of many particles, that's just the position vector of the center of mass and the g here is the acceleration and the g vector on top of it is the acceleration vector and the g squared is the square of it and you find that the Newtonian and the Einsteinian wave functions differ by the space vector. Now what's the t cube tell us? You see, if you were just doing an experiment like this, it wouldn't worry you. If you were doing quantum field theory, you would say, well, these things belong to what are called different vacua. They belong to... If you do quantum field theory, you have to worry about what vacuum you're talking about. This is one of the rules of quantum field theory, that you have to be a little bit careful about. And what you find out is that actually these two systems are equivalent in a sense, but the phase factor here is one which takes you from one vacuum into another. So it's cheating. Now, it's fine to cheat at this level because you can just stick with one or you can stick with the other, and that's fine. It doesn't matter. And that agrees with these observations and so on. However, let's do something a little bit more subtle. consider that it's not just the Earth's field we're looking at, but we're looking at, there was a big lump in our experiment, remember this lump, well that's a lump, and this lump might be in a superposition of two locations. Now if I'm pretending the lump's over here, then I've got one gravitational field, and I've got one vacuum to do it in. But if the up is over here, then I've got another gravitational field and I've got a different vacuum. At least I've got a different vacuum if I use the Einsteinian wave function. If I use the Newtonian one, I'd never have any problems. And so

1:00:00 who cares? You might say, well, good quantities just use the Newtonian method, which is the straightforward way. But if you come from the background of general relativity, as I do, I say, no, no, you've got to take into account of Einstein's theory which tells you that an acceleration and a gravitational field are equivalent. And if they are equivalent, that means you've got to take the Einsteinian view in taking the gravitational field into account. And so I'm saying that there are two different vacua, two different quantum field theories. I'm not allowed to make a superposition between one and the other. That's cheating. You get into trouble, you get into infinities, you get into inconsistencies. that is not going to work. For those of you who know about it, this is actually the Newtonian limit of a thing called the Unruh effect. The Unruh effect is something which enables you to explain the Hawking temperature of a black hole. See, a black hole has a certain temperature, which Stephen Hawking showed. It comes from considerations of combining quantum mechanics in general. Unruh and Paul Davies and various people showed that you can get the Hawking temperature another way. The Hawking temperature is something if you imagine a thermometer hold by a rope over the black hole and it would measure a certain temperature, which would be this Hawking temperature. But if the rope breaks and the thermometer drops into the hole, then the idea is that the thermometer, as it freely falls, would not measure a temperature. that the temperature is the result of the acceleration. This is called the Unruh effect. Now, the Unruh effect is usually done in proper relativity theory, but if you take the Newtonian limit, or the Galilean limit, you take the speed of light to go to infinity, you get just the same answer as the one I've been saying here. So this answer is also the same as the Unruh effect in the limit when the speed of light goes to infinity. So what I'm saying is that, yes, there is going to be, well, I should say that at the speed of light goes to infinity, the actual temperature goes to zero. So although there would have been an unruly temperature, that unruly temperature has gone to zero, but yet it's still a different vacuum.

1:02:30 Now this is sort of technical, so I'm saying it here, to those of you who are familiar with these things, and of course I can't go into the details here. is that you can look at what I just said from more than one point of view. You can either do it the way I did it here or you can go to this more sophisticated Anru and people's method of looking at, say, the Hawking effect considering how an acceleration gives rise to a different vacuum. If the speed of light which is finite it's got a temperature but the temperature goes to zero if the speed of light goes to infinity that is still, the effect I'm talking about here, we are a different factor. So it means that it's cheating to make this superposition. And then you say, well, how bad a cheat is it? Well, the bad cheat, the badness of the cheat is the coefficient of the t cubed here. So it's really this difference between the two genes squared, that's the problem, and then you just go back to the calculation I gave you before, let's see if I can find it where I will. but that's all I did this factor here I integrated over space and said this is a measure of how badly I'm cheating and so to get round the cheat you have to say that these states don't exist forever, there will be a lifetime and after that length of time making them one or the other will be a way of getting out of the problem it's not saying that's what happens it's saying that to become one or the other would resolve the problem And if you don't do that, you're in trouble with standard quantum mechanics. So if you like, I'm saying standard quantum mechanics with the superposition principle, as we know, and try to make the principle of equivalence of general relativity incorporate that as well, then you're in trouble. You land up with superposing two different vacuas, which would lead you to inconsistencies. And so to eliminate those inconsistencies, you can say, well, the state reduces to one or the other. And that's what I'm trying to claim is what happens. The point here is worth making, is if you do the Newtonian calculation, you consider a uniform sphere, and I've moved it by distance B, radius is A, and you can see that the EG, that's the quantity that you need to measure how quickly the thing will reduce,

1:05:00 reciprocal of EG tells you the speed at which it will reduce, you see that as you move these things apart, the EG increases. This point here is when they're in contact, and this is when you're moving them apart. So the basic point about this calculation is that the main effect is moving from superposition to contact. That's about twice as much as from there right up to infinity. So there's not much point in moving them very far. If you move them to contact, that's the major part of it. The point that you do have to worry about is the following one, that materials aren't uniform spheres. That's a Newtonian calculation, but really, this is the mass distribution. You know, that's the sphere, and up here I've got the distribution of mass, that's supposed to be uniform. But really, it's not like that. It's got lots of particles made of lots of individual mass units, which are the nuclei, and so the distribution will be very spiky like this. And when I displace it like that, the main effect will be moving these spikes apart from each other. Now, if these were actually delta functions, so those were point particles, moving them at all would give you an infinite effect, and so the EG would be infinite, and so therefore you wouldn't have any quantum mechanics, according to the schemes. So that can't be right. Well, it's also not what I'm saying, too, because what I'm saying is that you're looking at states which are individually on their own would be stationary. If they were to be stationary, they can't be delta functions. You have to solve the intruding equation, and you find there will be some distribution like this, where the mass in the nuclei has a little spread to it. So they're not delta functions. They cannot be delta functions and be stationary at the same time. That's a feature of the Heisenberg-Gunselt principle. So there must be a spread. So what I'm saying is that it's not the uniform case, it's not delta functions, it's something in between. So if you really wanted to work out, in fact, what this EG should be, you've got to do something like the bottom picture here. So there will be a spread. I can see now that this seems like to be moved up a bit. It will be something like that. And once you've moved it to about there, you're not gaining anything. So the main effect will be from coincidence, and there will be a little bit of effect where you're thinking about a displacement of the order

1:07:30 spread in the atomic nuclei. So that's the general feeling. Okay, well, is it true or not? Is this right? Or am I just walking around with nonsense? Well, we don't know yet. But there are proposed experiments. An experiment which I had some contribution right early on, but mainly it's these other people who do everything else. there was a particular paper where this was considered I don't have the reference here this has developed a long time this was some while ago I forget it was probably around about 15 years ago or so but the experiment is of the following time here we have a laser emitting a photon and the idea is you beam split the photon one part of it hits A lump, the impact of a photon on the lump displaces it, but the other beam split part of the photon goes somewhere else, and so the lump is in a state of being displaced and not being displaced at the same time. However, if you want to give any kind of significant impact to this, either you've got to use something like X-ray photons, and that was the original idea I had, is to use X-ray photons, and if you want to make them survive for long enough, you do that in space, I had a graduate student, Will Marshall, who was working with me and the two of them, in some order, came up with the idea, okay, you don't hit single, individual photons, what you do is you hit it loads and loads of times, the same photon. So here's the experiment. This is just schematic. The laser emits a single photon, something like visible light photon. It goes two ways. This one is kept in the cavity, it bounces backwards and forwards for as long as you want it. The other one goes another way, and there's a more sophisticated cavity here. It goes, you let it in, it hits this thing that's a bit like a diving board. Think of it as a diving board. And the photon is jumping up and down on the diving board. Each time it hits it, it gives it another little bit of an impact. It has to hit it about a million times,

1:10:00 a million times to give it enough impact so that this little mirror down here displaces enough so the nuclei here's a picture of what the nuclei are doing they get displaced by roughly speaking their diameter so this is a simplified description but it's roughly like that and the idea is that with a visible light photon or something of that general order that you could hit this little thing well this is a little mirror in one version of the experiment a 10 micron cube, so you would think of it as a little tiny cube whose diameter is about a tenth of the thickness of a human hair, just a bit too small to see, without a good powerful lens or something, and the photon hits that little mirror about a million times. There's a kind of hemispherical mirror up here, so it bounces backwards and forwards, And the idea is that if you can keep this going for something of the order of seconds to minutes, something like that, depending on the details, say a few seconds, and then, according to the theory, it ought to become one or the other. If it becomes one or the other, then you bring all these things back again, and you see whether these photons are coherent or not. If it remains a superposition here, it should be coherent, and then the photon will go back the way it came, and this detector won't see it. However, if this thing becomes one or the other, then half the time this detector will receive it. Well, that's a sort of idealized situation. You can make a better, more sophisticated looking picture, which is part of one in the paper. The reference is done here. This review, that was somewhere, but that was 2003. But the experiments have developed quite considerably since then. And Balmain-Stone has been doing this. Well, I saw him about three years ago, and usually he'd be very cautious about when he would say they'd get any answers. And then he said to me, spontaneously, without prompting for me, in ten years, we'll have an answer. And I thought maybe ten years, like these things, is a constant of nature, and he'd tell me the same thing every time. Well, I saw him again, two years later, and he said, again, spontaneously, without prompting, or eight years, we'll have an answer. That's pretty consistent. So I'm thinking, well, when was that?

1:12:30 It was about a year and a half ago, so it's about six years from now, maybe. Well, I was actually gratified that this is, in a sense, the most pessimistic case because, you see, how do you treat? There is a question which is a problem. I mean, how spread out are these nuclei? The worst case is if it's uniform. and then the effect will be harder to see. The best case is when you consider these as very, very localized, then you might see the effect sooner. So when he's saying 10 or 7 laws of the liberties, he's referring to the uniform case, so that it's a good chance that they might see it earlier than that. Well, that's the hope. Of course, if they don't see it, that's not so good for me. But anyway, I'm just trying to show you that it is a real effect that might be there or might not be there. It's real in the sense that it's experimentally detectable. So that's, we hope, that maybe before too long we'll get some answer. I might mention just a few other things here. How is the time? I probably run out of time. I think I probably won't. When did I start and when should I finish? One hour ago. More than one hour ago. Okay, well I should stop. But let me just say, I mentioned there are other things where you have classical alternatives where quantum mechanically you get the sums and the differences and you might have a situation where the classical and the quantum things are at the same kind of level. And I did consider a situation at this stage. I don't think I'll go into this in detail, but the situation I described to you is where the two locations of the lump had equal energies. But if the energies then the quantum mechanical expectation is it would oscillate between those two and then you might worry about what will happen, does it reduce to one or the other according to the scheme and I'm proposing here that it might reduce to a classical oscillation between two alternatives and that would be another way you might see this kind of effect I think I'd better stop there as I've been living on over time so thank you very much So, we can go for questions.

1:15:00 Roger, let me start the questions. Suppose the experiment actually works and is favorable to Europe in a few years. So they find a collapse, and not only the collapse is consistent, they measure the constant there, it's indeed the Newton constant that comes in, because there's a parameter, and everything else. Then, somehow, the theory needs to be put in a more complete mathematical form, right? So, on the one hand, the unit of issuing evolution has to be corrected, else involving gravity. So I guess the very first part of the question is how much do you know, what's your dreams about that? But the more specific question is that it's part of your idea that there are no large superpositions, that there are no superpositions of very different gravitational fields, very different space-times. this is where you presented it, there are superpositions of space-time next to one another. which last short, but they're continuously. So, space-time, if this is correct, is not just one space-time. So sometimes one reads Roger Pender's things that there are no superpositions of space-time. So I think this has to, correct me if I'm wrong, this has to made more precise. I suggested there are no large superposition of spacetimes. So then one still needs a way of talking about superposition of spacetimes, but still needs a way of functions over spacetimes and stuff like that. I quite agree. I completely agree. I'm not saying working in quantum gravity is a waste of time. Absolutely not. Because I mean, that has to be part of it, as you correctly said, that there will be, and you might consider situations where the deviations in the actual geometry is very, very tiny, but yet, and these things last a long time, and they could, quantum mechanical effects could be important, or there might be situations, as you say, where even if they last a very, very short period of time, those, those positions could have effects which are important.

1:17:30 so I think that, yes indeed quantum gravity is not important, but it gains in importance because we need to have a theory, I'm just saying that it won't be a quantum theory in the technical sense that it's a strict unitarity and that it won't be a theory which it is, as we personally understand the quantum theory, so it must have its reaction back on quantum mechanics, but nevertheless as one of the limits must be where the quantum regime is maintained, either because you're looking at very short timescales or because you're looking at very small superpositions, superpositions which are different from each other by tiny amounts. So, absolutely. And we're certainly looking for a theory which is overall has a consistency. So that consistency at that level must also be important. So it mustn't be that we just have a theory which works on where we're looking at the classical scale. It's got to be consistent at all levels. But I think we're a long way from a theory, despite all the great work, but certainly in the Luke community, I think my own view is that if you consider all the approaches to quantum gravity, that's the one which has had the most success and has the most plausibility. But I do think that it needs, again, to be thought of, in this context, that maybe we do have to think of quantum mechanics having its limitations as well. Another question? Okay, I may have missed something, but in the decay into one of the two, in a sense, Did you have any mathematical formulation for how this happened? Not really, no. You see, I'm not making any such a claim. It's a very limited claim I'm making here, which is that if you have superpositions of two states, each of which would on its own be stationary, then I'm giving you what I regard as a lifetime for that superposition. but it's very limited it's not telling you lots of dynamical things because they're moving in some ways it's certainly not a theory

1:20:00 which would incorporate quantum entanglements and how do you understand any of that I would say however that in my view you see classicality comes about in my view only because of state reduction the fact that we have about the classical limit, that when you think of large systems, they're really a great mess of superpositions and tangled states and all that. It doesn't look anything like the classical world. So we have to understand how the classical world comes about, and that I don't think can be understood purely in terms of conventional quantum mechanics. It's got to involve state reduction as being a process. But the theory is enormously far from giving you here is the theory. It's just saying in this very limited class of situations I'm making a suggestion as to how long you can have these two positions. But you see, I think it's got to be a major revolution, a really major revolution. And, well, you see, Newtonian theory lasted a long time. I guess the first break from Newtonian theory came with the Maxwellian notion of waves having physical existence on their own. So when Maxwell's equations came along, you had a bit of a deviation from Newtonian theory. But the major deviations didn't come until the 20th century. And quantum mechanics, well, how long has it gone? It hasn't had a century yet. So it's still a pretty young theory, and it has an internal problem, which Newtonian theory didn't. Newtonian theory was internally consistent. I think quantum mechanics has this measurement paradox, which in my mind is a genuine paradox, not just a problem. So it needs a new theory. So there's scope for new thinking. Absolutely. With clues, loop variables, I'm sure, is one area of clues, I'm hoping that Twisted is another place where you'll see clues, but I think that we need a revolution. Okay, now a question from the master's students. I'll give you time for the next one. It's a thing about one. Any other questions?

1:22:30 A very naive question, at the beginning you said that all the observations are fitting well with the true theory, and you said that the relativity accommodates well the cosmological constant. Then can you give your opinion that the fact there were so many rumors and it can be vacuum energy and any other interpretation of the cosmological constant and do you think that is something which is completely out of scope and it's not a good way to have a look in cosmology as a way to test something also in quantum mechanics? Well, I'm not quite sure I get the question, but I mean my view is, if you like, pretty old-fashioned on this issue in that I I have no problem with the cosmological... I mean, when I say I have no problem with the cosmological... I was pretty slow in accepting that it was really there, because certain technical things that I was doing depended on the cosmological constant being zero. And so I took a little bit of persuading that it wasn't zero. But I'm quite happy, and things that I've been doing later depend on the cosmological... The things I talk about on Thursday depend crucially on the cosmological constant being non-zero and being positive. So I regard that as part of Einstein's theory, certainly part of his 1917 theory. It's part of the theory that's described in all the cosmology books that I'm aware of, or the respectable ones, from that time onwards. So should one be looking for an explanation for the cosmological constant in terms of vacuum energy or something like that? Well, it doesn't seem to work. because you get up by 120 powers of 10 or something. So I think there must be some other explanation for it, but the explanation, in my view, it could perfectly well just be it's that term in Einstein's equations. Of course, it doesn't tell you what its value is the value it is, but it's only one of these rather strange things that you see in physics where you have very large numbers coming into physics, And this is just another place where you say, compare it with the Planck units, you see some factor of 10 to 120 or something, which is a ridiculously large number.

1:25:00 But we see large numbers already, as Dirac pointed out a long time ago, and you see numbers which are powers of 10 to 20 coming in. the force between the electron and the proton and the hydrogen atom the electric force is about 10 to the 40 times the times the gravitational force and so that's a big number well 10 to the 120 is the cube no explanation but nevertheless the fact that we see these absurd large numbers in physics only made a little bit worse by the fact that the cosmological constant seems to have an even rather larger power of these big numbers coming in. But I don't regard it as... I regard it as an extension of the mysteries we already have of the large numbers of physics. I'm not sure if that was your question. My question. I find if I want to have values that are necessary in the physics, and I have the impression that the cosmological constant is something we measure, but we have no feeling, and have no... Well, it plays a big role in what I'm going to talk about on Thursday. But of course, I think we'll find it's more important than we see at the moment, that it has roles to play physics also. But since it has such a small value, if you like, it's hard to see what those roles are. They're not very direct. But they certainly change the meaning of things like what we talk about in scattering, you see, put things in momentum states. Well, what's the momentum state in cosmology with the meaning? So there are all sorts of ways in which it does affect the way we look at physics. And I suspect that will become more of time. But I certainly agree that it's something that as far as present understanding is concerned, it looks like something we didn't need. And why do we need something which has such a small value and why it has a value which

1:27:30 we happen just to notice at our present stage of existence and we see that it contributes to the rate of expansion of the universe but what else? But I think that's, in my view, it's a sort of temporary situation we will see its importance grow. But that's just the speculative comment. Do you think that the objective reduction discussed can be described in terms of the Newton-Schweddinger equation? You're referring to the thing that, well, people have played around with it, and I do too, with the thing I refer to as the Schrodinger-Newton equation, which was partly needed for this scheme, because I didn't go into that. But if you want to know what a stationary state is, you see, a stationary state, technically speaking, according to standard quantum mechanics, is spread uniformly up the whole universe. It's an eigenstate of a time operator. And that's not much good if you want to talk about a little lump sitting here. So how do you talk about a little lump here being in a stationary state when in standard quantum mechanics that stationary state would be spread out and ruin the universe? Well, that makes no sense. So, however, if you modify this Fourier equation in this way by introducing a term from the gravitational potential, then you can consider these states as solutions to those equations. And that is the way that I would, I suppose, say, do this calculation. Consider those things as stationary, in that trading and using framework. But whether you can address the actual collapse within that framework, I know some people have ideas in that direction, but I could never quite see how to incorporate that and make an actual equation, a dynamical equation for the collapse from that perspective. Maybe that could work. I think some people have made suggestions in that direction, but I'm not sure about it. Just like maybe I didn't understand correctly, but what you said is what you're proposing is basically to solve the paradox about the measurement, but it seems to me like you didn't solve it, you just pushed it to some time.

1:30:00 Because what happens if you measure before your proposed state decays? you can imagine an experiment you do it fast enough and then you're back to the same problem I should have let me just interject something here I should have said something which I omitted to say which is that in most experiments or in most situations I would consider that the major effect is in the environment so if you have a quantum situation a superposition which becomes one or the other there's the conventional view that people say well it's environmentally coherence and it's the states in the environment which you lose track of and that means you effectively have a reduction well in a certain sense I'm agreeing with that because I'm saying that all that goes a little further here, I'm saying that yes the major thing is the entangled environment and the most the major mass displacement will be the environment. So in almost all situations, it happens randomly in the environment. You have to, to see in this experiment, you have to make sure the environment is cleaned out as best you can. You have a near-perfect vacuum, you have to reduce all your vibrations down near to absolute zero, and so on. Otherwise, you'll mark it up. Now, in preparing a state, which I think is what you're talking about, you have to take advantage of this, because if you want to think that your state is initially in a pure state, I mean, there's a bit of a paradox there, because Hawaii isn't entangled with all sorts of other things. And strictly speaking, quantum mechanics, I don't know how you deal with that, because you would say, well, this state isn't a pure state, because it's all mixed up with all the environment, and you say, well, I don't care about the environment, because I've done some experiment which somehow allows me to consider it to be an actual pure state. Well, I would say that you're doing that because you've spilled all your unwanted degrees of freedom into the environment where they reduce to something which is your pure state. How that happens in detail, I think, is an interesting question. You look at the exact experiment. How is that being done? Well, my view would be that it's always because the state reduction has happened spontaneously, the

1:32:30 cause of the environment has reduced the state and it's become one particular thing and then you can treat it as a pure state. And if there's a bit of cheating going on, even in conventional way of looking at things, because why is your state, why are you allowed to treat it like that? Why is it a great entangled mess? And I think that in principle this gives you a way of dealing with that, because you say, well, if you have two alternative things, you might want to start with and say, I'm choosing this one and not that one, because this one is being entangled with things, to make a big effect which reduces it to that so that the reductions already happen to put it into the state which you consider as the initial state in the experiment. But I think it's a good question which needs to be looked at in detail on what you're really doing but it's not just affecting me I think it's more serious than standard quantum mechanics that would be my Any questions? Let me ask another thing. In the proposed experiment, if I didn't miss any... I don't think it looks anything like the one I was showing you, but it's the same idea. No, I mean, you have this solid, and the nuclei can stay in two different positions. So you need this as pure quantum states. You treat them as pure states, yeah. Yeah, and if the Gerard-Dremini-Weber idea is correct, you have a decay time of these states, so you should also take into account this fact. I mean, if you have a large number of nuclear, you have a decay type, for instance. Only for each one separately? Yeah. Ah, no, but you'll consider them entangled. So you want to have something which is sort of like a crystal or something, which is very rigidly behaves as a unit. So the whole thing must be a very rigid system. Okay, there will be individual vibrational states, too, but you won't cool those down so the individual states are you put it in the ground state

1:35:00 as far as the individuals are concerned but there is an overall motion so there is a question I guess this is technicalities which I don't fully understand but one of the reasons for cooling these things down to a cryogenic temperature is you want to get rid of all these individual excitations and make the whole thing behave as a unit. I guess there are technical issues about how you do this and when you've done it, which certainly I wouldn't know, but I think that's the general idea. So the lowest mode, you could it down below that. So you're looking at the whole thing, the translational mode of the whole thing. any more questions okay so I think the all-mask students okay so let's thank our speaker again so just a brief announcement so remember that Thursday we have a public talk by Roger Penrose but it's going to be in Amphi 6 of the university which is right on the other side of the road I'm going to get to be already in case because I'm a bit of the number 6 thank you Thank you. So in this, with this mechanism, the probability is not annihilated, it's just a return to

1:37:30 I mean it's not saying anything