Time & Deep Structure of Dynamics — Part 1

0:00 Thank you very much. Now, I hate speaking into a microphone and I like to wander around. John Ehrman, could I just check you can hear me clearly? Yes, fine, thank you. Paul Davis was the rich in, well, first of all, let me just say what a great pleasure it is to be here in Kirchberg. My wife and I are entranced by the place. It's wonderful to be here. we're going to stay the whole week. We won't be coming to everything, but we'll come to quite a lot. Paul Davis should have been giving this opening address, but he was unable to come fairly late. He discovered that was not possible, so he asked me if I would stand in, and I said yes, I'd be delighted. Now, Paul, about eight or nine years ago, published a book called About Time, and in the preface he says, if at the end of this book you're still confused about time, don't feel bad about it. I myself was more confused after I'd written the book than before I'd wrote it. Now, I'm sure if Paul had come and spoken here, he would have spoken about the notion of time that has dominated the last century in physics at least. That's the notion of time that Einstein introduced. I'm going to come to Einstein's notion of time rather late. I'm going to talk more about what, above all, Leibniz and Ernst Mach said about time and show that really what they said about time you can put that into a theory of dynamics into the way the universe works and in the end it turns out to have a very interesting relationship to the way time is treated in Einstein's theory and the bottom line of all this is I want to try and persuade you that there's a very great likelihood that time really does not exist at all, that it's a completely redundant concept. And I think the confusion that Paul Davis was talking about is the mistake of thinking that time is a real thing and exists. It's something quite different if you can say that it's anything. That at least is my view. Now, everything really in the

2:30 discussion of time within dynamics and within modern science has to begin with Newton. Now Newton got from Galileo and I think even more from Descartes the notion of the law of inertia which Kant described as the most fundamental law of the basis of natural science. According to this law, a body left to its own would travel at a uniform speed in a straight line forever, unless it was acted upon by other forces and deflected from this rectilinear motion. And Newton felt that this was a wonderful basic law, the first law of motion. And adopting this law of motion and just the notion of forces which deflect bodies from this rectilinear motion, he had this incredible coup of being able to explain the laws of planetary motion that Kepler had found some 70, 80 years before Newton did his work. So Newton felt that it was absolutely essential to have a framework of dynamics in which the law of inertia could be formulated and made sense. And Newton, like all his contemporaries, like Descartes, like Leibniz, wanted to put the science of dynamics on an axiomatic foundation, absolutely crystal clear and as secure as the axiomatics of Euclidean geometry. So that was his ideal. And he thought that this could not be possible unless there was some huge fixed space in which objects move. And therefore he imagined a space which is really like the space created by the walls of this room. We can talk about straight lines in this room because you can see they're straight relative to the walls of the room. So that was the first thing he imagined was there was this thing that he called absolute space. And he was hugely excited with what he thought he'd found evidence for the existence of this thing, and he called it the sensorium of God. He was so impressed with it. And in addition to that, if he's going to say that a body moves uniformly in a straight line, he's got to have some sort

5:00 of measure of time to say what it is. Now, interestingly, and very appropriately for my subject, there is no clock in this room. But just in case I don't go over my allotted time, I put my watch down here, you can imagine time in Newton as some mysterious absolute clock hanging on the wall which is just ticking away and objects moving on their straight lines in their law of inertia in this room are just moving at a uniform speed as measured by that clock on the wall. Now there's something very mysterious about this absolute space and time is that they're both of them completely and utterly invisible. And Newton was very well aware of this. But he argued that you could, from the things that you could observe, which are only relative, how far I am from Professor Weingart, that is observable. And so is my watch. of the clock are moving around and the cogwheels are going inside it no well it's actually a quartz clock so it's not quite like that but anyway those are relative things those are sensible quantities that you can see so the Newton argued but he never really established it in his work and amazingly nobody has ever taken the trouble to do what Newton said he should do which is to show how you can recover the motions in absolute space and time you can observe. And this was a problem that he posed at the end of his famous scolium in the Principia, where he said that he actually wrote the Principia to show how this is done, but he never returns to the topic. So that's the review of Newton. Now let me come to the famous reactions. Any of you who've studied a little bit in the philosophy of science, I'm sure we'll have read the Leibniz-Clarke correspondence and also perhaps Ernst Mach's famous book on mechanics. So I want to put down some quotations if I could just read them out to you. Leibniz said, I hope space to be something nearly relative.

7:30 And so he's really getting down to ontology. saying there is only relative things. Let me just bring that up. Here is a triangle. By this triangle, I want you to imagine that there's three material points, one at each vertex of the triangle. Now, according to Newton, when objects, when those material objects move around, they move in absolute space, which is ontologically there, and first they can move is, first of all, they can move relative to each other. The triangle sides, the ratios of the sides can change, the triangle can get bigger and smaller. And in addition, the centre of mass of the triangle can move in three directions in space, and its orientation can move in three directions of space. And all of those things are, so to speak, real according to Newton. But Leibniz is saying, no, that is quite wrong. The only thing that is real are the relative quantities. It's actually the triangle. And when he says space is the order of coexistences, he's pressed later in the correspondence by Clarke, what does he mean by order? And he says, I mean the distances between the particles. That's what is real. That is the order of the things. And space is just a summary of all of these relations of distance between the objects there. That is the viewpoint of Leibniz. and Marx says very similar things years later now let me just say that Leibniz made very powerful criticisms of Newton's ideas at a philosophical level but he made no attempt to set up an alternative dynamics which was based on his underlying ontology of relativity things come. And looking back with the hindsight of history, you can see that it would have been completely impossible for him to do that. The technical means did not exist in his time to do that. A lot of Leibniz would have created them. Now, Mark went much further. And he, first of all he repeats the sort of criticisms that Leibniz made now I should have said

10:00 Leibniz's view on time Leibniz says there isn't a so to speak a clock out there ticking away all that happens say if you just had the three bodies is that at one instant they form this triangle and then at another they form another triangle, which is slightly different. And all you have is just a succession of different configurations of the three bodies, different triangles. And you must just think of them as one coming after the other. This is what he means by the time is an order of existences. The distances of the three bodies are the existences, and the time is just the fact that they follow each other. And I can illustrate this here, you to get this really firmly in your mind, you could, let's do it in red. Now I'll keep to green for a minute. This could represent one triangle, another one, another triangle. Each point along this curve represents a triangle. And Leibniz is saying that that is all that there is to the world. There is nothing more than that succession of triangles. Whereas Newton would say that the history of those triangles as they evolve in space and time there's a little red spot saying this is this is the instant now this is now this is now and sometimes that red spot is moving a little bit faster along that curve the triangles are coming up faster and then it's going slower so you could imagine the Newtonian picture is this curve and there's the red spot going along it at a different speed. That's the instantaneous now. But the Leibnizian view is much more a timeless one. As Kurt Vonnegut said, it's like seeing the rock is all at once. All the instants of time are sitting there all at once, if you like. You can imagine each triangle defining an instant of time, but they're all there at once. Now Mark, in one of his most famous sayings, is really saying very much the same thing. But he's emphasizing Somehow or other, from the changes of things, we've got to deduce the time that we use. Why is it that we use this clock and say this is a good watch and keeps good time, whereas some other measure of time is a bad one? Muck is already, he was one of the greatest experimentalists in the history of science. He very nearly got the Nobel Prize for his work on the shock waves.

12:30 So Mark was acutely aware of making sense of things from the experimental point of view. So he's already hinting that we need to understand how the measure of time that we use, the time that actually appears in Einstein's theory as well as in Newton's theory, how that actually comes out. We need a theory not just of the succession of instants, but duration. In some senses we want to know how it is that nevertheless we do say that there's a year between here and here. And these are two more very famous sayings. This is just again insisting that only the relative motions count the second one there. and then a feeling that you get very much from both Leibniz and Mach is that the only way to understand the universe is to consider it in its totality. Just, it's the absolute opposite of the atomistic viewpoint and the completely reductionist viewpoint that is due to Descartes and Newton. The Newtonian viewpoint is that really the most important thing in the universe is absolute space and absolute time, but particularly absolute space. And then you can think of an individual particle, and that particle is forced by absolute space to move in a straight line in it. And so the world is completely broken down into atoms. And it is no accident that Leibniz and Muth were perhaps the two greatest opponents of the idea of atoms, this particular idea of Cartesian-Newtonian materialism that there are atoms moving in space. Of course this goes back to the ancient Greeks, Democritus and others. And you will find whenever you read Leibniz and Mach this constant reference to the universe as a whole, the totality of the universe. And that I think is essential if we're going to develop a really deep understanding of what time and motion is. So it won't harm to read that one there Mark Neon.

15:00 Now, I'm going to tell you how you could set up an alternative system of dynamics which just uses the relative quantities that Leibniz and Mark said you should. And show, in fact, that it turns out that in a very pleasing way, both Newton and Leibniz were right. But the Leibnizian element that comes in is very important and goes to make dynamics much more precise and much more strongly predictive than it was in Newton's hands. And we'll see how that happens. So these are principles which I've really taken from Leibniz and Mark, people who are quite an art to get this view graph in the right place. That's it. The first one I've already hinted at, but very important is to say that it's a closed dynamical system. Now this is undoubtedly a weak point of the scheme that I'm going to propose to you. The basic idea is that in some senses you can meaningfully talk about the universe as being a completely self-contained, closed thing. In Einstein's words, something in which the circle of cause and effect is closed. You can find a cause for every effect. And there have been two very significant and very suggestive models in the history of Western thought enclosed and self-contained. The first is the spherical universe of Aristotle, and 2,300 years later, the spherical universe of Einstein, the first cosmological model in the theory of relativity. And it's not an accident that happens. I think it is almost a necessity of thought that if you want to have a completely enclosed system, you always are striving to understand things as deeply as you can, you have to postulate in some senses the universe is closed. However, Einstein's theory, although he himself was immensely attracted to this idea, and that's why he created his famous model in 1917 of the closed universe, his own theory allows a completely infinite universe. And, well, these Machian principles go through a long way, but there's always something out at infinity that you

17:30 and that's a bit unsatisfactory but still it's worth the exercise of going through it but that is an important conceptual part of the story certainly it's important to have geometry in this thing Galileo said he that attempts natural philosophy without geometry is lost I think this is one of the really great true sayings of science and really dynamics as I've already said the attempt, this marvellous achievement of the 17th century to move on from geometry to dynamics and putting it on an axiomatic basis. So the foundation of everything will be geometry and on top of that we will build up dynamics. Now, Leibniz had two great principles, I'm sure as most of you are philosophers, you'll be familiar with them. One is the identity of indiscernible. He says that if there is something and all its attributes, if you imagine two things, let me start again, if you imagine two things and say that they are different, but all of their attributes are identical, then that is nonsense. If all of their attributes are the same, they are the identical thing. And I won't go into any more details about that, but all, what that does mean is that according to Newton, this situation with this triangle here, or here, or in that orientation, or a bit bigger, or a bit smaller, but the ratio of the sides remaining the same, those are different situations according to Newton. And Leibniz is saying that is absolutely not true if you are considering the whole universe. And that's a really key difference there. And you can make, I won't have a chance to go into all the strengths of the principle of the identity of indiscernibles, but it's an absolutely key underlying philosophical the next one I want to say and you can think of this in terms of

20:00 just again my three particles the three body problem the famous problem of the earth, the sun and the moon which gave Newton headaches, it was so difficult this is if we're talking about that in terms of Euclidean space we're in the geometrical world that Newton inhabited Leibniz, if you take Leibniz to his limit and mark, you would say that all accounts is the triangle, and not just the triangles I hold it to you here, but any triangle which is the same shape as this triangle, but either smaller or larger, if that's representing the whole universe, the complete dynamical system, then those are the same states. so the space of states of my three particle universe is all possible shapes of the triangle and that's nothing more, nothing less so there's just, and that's actually a two dimensional space the shape space for three particles in the Leibnizian world has two dimensions and that's the world in which things happen so that when I drew this curve here really this is a curve properly in two dimensional space each point in here could represent a shape of a triangle we're going to talk about the dynamics of pure shape only shape counts well there will be masses because masses is an important part of Newtonian mechanics but even masses are on their way out really in modern physics so it will be only shapes that count I've already implied it here of the universe is a continuous curve like that in its shape space. That's what physicists call the kinematics of the situation. I haven't talked about any law of physics about this. I've talked about geometry and about what is, so to speak, real. Now, Leibniz also said that you must never introduce something arbitrarily there must always be a reason for anything that happens there cannot be an effect without a cause and some of his most forceful arguments against Newton in which I would say he was vindicated centuries later by the discovery of quantum mechanics I won't go into it

22:30 but there are some very impressive indications of Leibniz's viewpoint. You must find some sort of reason, you must have some sort of principle that underlies everything when you're going to find an explanation for the world. The world must be rational. Leibniz was the supreme rationalist. And as I'm sure you know, not even God, according to Leibniz, can escape the dictates rationality. There must be a reason for everything. And he was quite unlike Newton in this respect. Newton's God was very much the Old Testament God who was pretty bad tempered at times and would intervene in the world and sort things out if he felt like it. And he was free to do it. And his will was arbitrary. And Leibniz said, no, that's absolutely not the case. So we've got to have some principle. And Leibniz says, You've got to invoke something that goes beyond pure geometry when you pass from geometry to dynamics. Geometry is about sort of things that we can see about shapes and about numbers. Since Descartes' work on geometry, it's really about numbers. Descartes reduced geometry to numbers. So Leibniz said we need some principle. And the step from geometry dynamics requires us to find some principle that's going to say why something happens rather than something else. So the question is, why does this curve in shape space take the particular path in shape space it does? This is a succession of shapes of triangles. Why do we have that particular curve rather than another? And the principle I'm going to propose is a very simple one, and it's right sort of in the thing. Suppose I start off with a triangle of one shape down here. This might be the equilateral triangle. And I've got another triangle of a quite different shape up here. now these two triangles I could imagine a history where these two triangles are joined by all sorts of curves here's another one going up here like this and there's infinitely many of these curves

25:00 how am I going to choose the actual one that is realised between there I've got to have some good principle for doing that now what I'm going to propose and it's very close to the fundamental principle It is a form of the most fundamental principle of theoretical physics, I would say, the principle of least action. If you want to walk about the mountains here, between any two points on the curved surface of the mountains, you can find the shortest path between two, as long as they're not too far apart. I mean, you walk right round the world and you get what's called an extremum. There's a very long way round the earth, but there's a shorter way. two points, in general, there's just one shortest path on a curved surface. And this is, and finding that shortest path is called a geodesic, I'm sure you know that. A geodesic. what you what you want to do to define a geodesic law so the basic law is going to be the curve that is actually realised the history that is realised is a geodesic law but to have a geodesic law you have to know what is the distance between any two neighbouring points any two infinitesimally separated points so I'm going to have the task I've got to do is to have a shape of one triangle and a shape of another triangle which is very nearly the same the angles that define the shapes of the triangles are only slightly different and I've got to be able to say what is the distance between those two shapes because then I've got a geodesic principle here and I can find out the shortest path between those two shapes that I've marked in red there I hope you can see those red bits at the back, but you can imagine those if you can't see them in your mind's eye. So that's the task. So now I'm going to tell you how that's done. Using only these two triangles.

27:30 Now first of all, I'm not going to take account of changes of shape. So imagine that, first of all, changes of size, changes of shape are the only things that are real. Changes of shape, there's nothing real except changes of shape. But I'm not going to, for the moment, consider the problem of changes of size, where the triangle keeps the same shape but just gets bigger or smaller. Now, let me put a particle of mass, some mass here and some mass... So, I told you, let's take all the masses equal for simplicity. So, there's a mass of unit 1 here and here and here. And there they are in a different triangle somewhere just a little bit further along my curve. And I want to be able to say what's the distance between those. So what I'm going to do is I'm going to take the one triangle and I'm going to call this process best matching. And I'm going to assert that the two most basic principles that govern the way the universe works are the following. First of all, it is a geodesic inner-shaped space. Now this is a conjecture, and according to the best evidence we have from Einstein's theory at the moment, that it doesn't quite go as far as getting to shapes only. There is a failure of Einstein's theory to be what is called scale invariant, which I think is very challenging. This is in fact what allows the universe to expand and the Big Bang model to make sense within Einstein's theory. Now, apart from this thing, which is in fact an incredibly tiny little defect from the point of view of Leibniz and Machian philosophy, you can understand everything that we know about the classical dynamics of the universe in terms of just two ideas that it is meaningful to talk of the distance between two neighbouring shapes and that basically what is underlying the dynamics is some principle of least action some geodesic principle and the key to finding that the distance between two shapes. So now I'm going to show you what that law is like. And

30:00 as I say, this is approached straight out of the textbooks of Leibniz and Mach. And I probably won't be able to get round to showing how, and certainly it's far too technical to show how this is realised in general relativity. But the two principles that I've outlined to you, I assure you, are sitting right in the heart of general relativity. You normally don't see them because Einstein created with Minkowski this wonderful notion of space-time, a four-dimensional space. And in that language of a curved four-dimensional space, you don't see these two principles at work nearly as well. You see the first principle, the principle of least action, at work very well. That was formulated by Hilbert and elaborated by Einstein of it is is at work but this idea of what i call best matching the way the separation is is determined between two three-dimensional configurations of the universe is not brought out nearly so clearly so the uh the idea is the following so i've got for simplicity unit masses here and and i've got somehow or other to define a distance between these two triangles so what i following I just take my two triangles and I place one on top of the other in a completely arbitrary fashion and then I measure these distances which are the distance that this point one seems to have moved relative to where it was here and now it's here so there's a distance there and there's a distance here and there's a distance there so I take that distance and I take the square of it I multiply it by itself and I do the same for this distance here and I do the same for the distance here so I've got three squares of those so I add up those three squares and then now I apologize for somebody who's heard me say this before if you were told that if you hadn't got the solution to the problem by tomorrow morning you were going to have your head chopped off, I'm damn sure you would have the answer by tomorrow morning which is that you move these two triangles around until you bring them into

32:30 the best matching configuration where that sum of squares is minimised and that exists, that's a positive definite quantity that exists and that's a system that's that will save your head, think of Rumpelstiltskin the fairy stories we've had mentions of that that will work and that is actually the dynamical principle that underlies general relativity subject to certain qualifications but the the most I think the most clear way of asking of thinking about what is going on in general relativity place like that it's immensely more complicated because we're talking about comparing not just two triangles but two three geometries where the geometry is curved you know that Riemann introduced Gauss and Riemann introduced curved geometries and there's one geometry and another geometry and they have different curvatures it's like waking up and finding that all the mountains around Kirchberg had changed their shape a bit next morning and so does this picture we've got of Kirchberg and another one tomorrow which is slightly different and you've got to compare those two complete landscapes and that's obviously much harder but it's perfectly possible to define an analogous procedure and do it so that's basically what the what the idea is now Now if you do just that, that will give you, and we haven't yet worried about the business about changing the scale, changing the size of the triangles, that alone will actually give you Newtonian motion, inertial motion of those three particles, subject to one very interesting restriction. You recover Newtonian inertial motion in something that looks just like absolute space. Out of that principle, you recover the relative motions, but there's one thing you don't get. According to Newton, there is a thing called angular momentum. This is a very fundamental dynamical quantity. Probably all of you will have heard of it once. It's in some senses a measure of how much the things are rotating in absolute space.

35:00 This is why the Earth is flattened somewhat at the poles and Jupiter so much that you can see it when you look at Jupiter through a telescope, even more spectacularly the spiral galaxies these these have got angular momentum and that's what's flattening them out according to this prescription a universe that is described in this way the complete universe can have no angular momentum at all so that if the universe was just something like a globular cluster a million stars in in euclidean space described by this law it couldn't be a spiral galaxy because that has angular momentum. It would be looking like an elliptical galaxy, spherical shaped. And that's why I say that these Leibnizian Machian laws are more predictive than the Newtonian laws. Now, it turns out that in general relativity that's already contained. There is a deep sense in which the universe cannot rotate in general jump up and say, ah, yes, but Gödel's universe does that. The matter in Gödel's universe is rotating. Yes, but there is a, well, there's various restrictions about that. But there are certainly models in general relativity where it definitely looks as if the matter in the universe is rotating in one sense. But as John Wheeler pointed out 40 years ago, and so did Hernell and Danen in Germany, if you look carefully, you can see that there's a certain sense in which gravitational waves are rotating in the opposite direction and the net effect is exactly zero and this again must be where the universe is closed where it's not one of these ones that goes off to infinity where the where the concept is much harder to discuss so that's really what's what's going on now if you want to get interactions gravitational interactions that's relatively easy to do and you just there's a thing called the newtonian and you just actually introduce that into the theory in exactly the same way as it's done in Newton so that you can recover all of the Newtonian interactions without any problem. And the reason why that is the case is that the Newtonian gravitational potential, as you know famously, is a one upon our potential. The gravitational potential between two objects goes inversely as the separation between them and the force is inversely as the square of the distance.

37:30 know surely the inverse square law of Newtonian gravity. The forces in Newtonian gravity are completely acceptable to Leibniz and Mach because they depend only upon the relative separations. But they're not acceptable from the point of view of scale invariance. If you say only shape counts, if I take this triangle, it has a certain gravitational potential. If I increase the size a great deal, you get a lot the gravitational potential it's negative so it gets larger it's really bigger than zero so as you pull the objects apart the gravitational potential goes down so there's an issue with making the theory scale invariant now I think I'm not going to go into any more details to say that you can put this through through first of all in the context of newtonian point particle dynamics where we start from right from the beginning by assuming that space is euclidean and we talk about particles moving in euclidean space and if you put through these ideas that only shapes count you recover newtonian theory but in in very special cases you can actually exactly recover newtonian theory with gravity and electrostatics exactly as in newtonian theory you cover recover the law of inertia exactly as in newtonian theory you also get some one thing more if you this is very interesting if you have globular clusters and this i may say this fact that i'm talking those with Einstein's 1917 paper when he created his famous cosmological model which very much concerned Einstein globular clusters look as if they're held together by the gravitational forces they're like the solar system the gravitational the energy is negative and it looks as if they will be held together but every now and then one of the stars in a globular cluster very close to two other ones and you have what's called a three body collision and one of those three stars gets a lot of energy a high speed and is thrown out of the globular cluster and goes off

40:00 to infinity, it escapes and this is called the evaporation of globular clusters, it's a very interesting phenomenon according to standard cosmology the globular clusters which have half a million, a million stars in them were formed very soon after stars were formed 10 billion years ago or something like that very ancient objects but they're very slowly evaporating they're slowly most of them have lost about half the stars they started with and when we go on another 10 billion years they'll have disappeared from the universe according to the standard scenario and this is a feature of newtonian dynamics which comes about because it doesn't have this property of scale invariance size counts in newtonian dynamics and it also counts in einstein series because that's why the universe expands according to his theory but in this theory there is a sense in which that cannot happen, the universe is bound in an ironic sense to stay the same size you can't have things escaping what that means if you want to put it in shape terms is that if you have two stars here, the third one cannot go so far off that the ratio of this distance to this one becomes infinite. It must, after time there's an extra force which pulls it back again. There's an automatic adjustment mechanism which stops that happening. So that's interesting. So that's all there. And as I say this, let me just say about Einstein's theory. In Einstein's theory, where space is three-dimensional at any instant of time, which is defined in many different ways in Einstein's theory, you can blow up space at each point. Just like here, you could imagine here, it's slightly misleading for those who really know, but it's not a bad example. you could imagine a mole well there is a mole hill there I can see it from here a mole comes up and heaps up the surface of the thing and so the shape so to speak we had a surface which was a certain surface like that and now the mole hill is there and that's a bigger surface the hemisphere is more than the area through the equator so in fact that's a local change of the size of space so this is the wonderful thing about

42:30 three-dimensional Riemannian geometry you can change the size of space at each point and at any point in a Riemannian geometry two quantities determine what is called the shape of space at that point and the third one describes its local size and therefore you can do infinitely many changes to a Riemannian three-dimensional geometry in which the shape is constantly being changed differently and independently at each point of space sorry, the size is being changed independently, whereas the shape is not being changed. So the shape that's what's called the conformal structure. The conformal structure is completely unchanged and the local sizes are being changed. And you can do that with Riemannian 3 geometry. And the wonderful thing about Einstein's theory is that formulated in these terms, it allows all of those changes of size locally to take place provided the total volume of the universe is not changed by that process there so that there's a very strange thing in Einstein's theory that size locally does not seem to have any effect dynamically but just that one thing the total size of the universe is meaningful it's a very mysterious property of Einstein's theory and if you describe the size of space in newtonian theory you need an you need infinitely many quantities one at each point to say what the local size is at each point and then just one more quantity which tells you the total size and the only thing that counts dynamically in einstein's theory at least the standard cosmological models in the closed universe case is that overall size It's very, very mysterious. And I will risk, stick my neck out and say, I think Einstein's theory is wrong for that reason. But it's one hell of a risk I'm taking in saying that because it means that the Big Bang theory is quite wrong, that there must be some quite different other interpretation for the Hubble redshift. Now, if you look at standard cosmology, what is happening in standard cosmology is that the universe starts off in an extremely uniform state where everything is close to each other. And since then, it has been expanding, and at the same time, it's becoming much more variegated. Clusters of stars are forming, structures, human beings are forming.

45:00 Structure is forming all the time. In a dynamics of pure shape, the only thing that can happen is that the universe becomes more structured. and therefore I will make the following prediction. There is a theory out there which I believe is the theory which does describe the universe and it is one in which the change in the structure, the growing richness of the structure in the universe induces the Hubble redshift by a mechanism which I can't put my fingers on and nobody else can but nobody else is seriously trying apart from myself and a few collaborators but that is the said is correct that is that's okay by the way the basic facts behind this came to light a good 30 years 40 years ago with work by somebody called jimmy york in princeton with john wheeler who is the person of course who coined the expression black hole and many other things i think he has 27 coinings in the anglo-saxon literature to his name also a very big figure of course in the development of the hydrogen bond I'm going to finish now with just saying a little bit about what are the quantum implications for this as it's I've been going for about 50 minutes I think see I still practically use these things but I can see this thing I can pick up this thing I can see it working and how its parts are related to the rest of the universe