Quantum Computability & Nonperiodic Tilings as Nonlocality (contd.)

0:00 And the normal way of describing quantum mechanics would be, let's imagine the spread of heat here, and the observer there, equal time slices. And then that operation to this observer occurs first, that one suddenly affects the state on the other side, and the second operation is then measuring the state. So that would be the picture this observer would have of reality. Now we think of this as another observer moving in a different way, and the other observer this observation gives first, and this reduces the state on this side, and this one is now observing a different state on the other side. Well this is only indicating a number of things, sort of the non-locality that one has, somehow these different things are not separate. Emphasizing that there's a basic conflict with relativity. You want a picture of what could really happen, and some people give up and say, well, you're not talking about reality, and so on, and I think that's a rather dangerous view to hold with physics, but nevertheless, there are very much serious problems about how the picture's reality, and my own view is that this indicates that there's something about the way in which space-time is treated in quantum physics. In fact, even observations of this sort, one has to bring in the quantum treatment of space-time, so somehow the alternatives coexist in some way before the observations are made, and space-time as a whole has to find a role for itself. That's exactly how this would take place, but not some monotistic theory. I want to say a few words, but I'm going to have to cry. But my reversibility was, this is only a rapid mention of what I thought was a big different lecture than you can see, because I, as the new second law of thermodynamics, I hope did not describe that slide.

2:30 Let me describe this one instead, which is a picture of the universe, or two pictures of the possible universes. To get it to close, let's only quote about the first case. This is meant to be a space-time picture, and the point is about the second law of thermodynamics, which is what my other slide will be about, is that somehow the universe started off in a very, very special state. And that's really what the second law is telling us. The entropy was very, very small in the beginning, which has been going out ever since, and that means that the universe started in a very, very special state. And I've drawn the 19th law. If you look at the Big Bang, you may think the Big Bang is an awful mess, and in fact, what, they need to be tied, and that's where you get the second law. But if you have this closed universe, the entropy keeps going up and up and up, and you do have an awful mess at the end. It would be a big crunch, but the Earth's universe would be collapsed. But what is puzzling about this picture, and where the second law comes from, is that the Big Bang is not also a big mess. And the most likely thing would have been a big mess, because that's high-energy. So what is it that's so special about an event? This is an inevitable situation. If you get that and go from there too, then you have no second option in the next. You have white holes, you have black holes, you have no black holes. In gross conflict with observation, what we appear to see is something like that. So I have a picture of Darwin, of the creator. Choosing the universe, out of all possible universes, that's the main question, the phase of all the universes, the picture is supposed to indicate that the creator has also sort of created phase space as well, but there is also a particular point in phase space being selected, and the point is, how accurate does the creator have to be on that? So if you take a universe, which is the thing that you have, then the volume that it has to be aimed for as a fraction of the entire volume, It's one part in 10 to the power of 10 to the power of 123. It's an enormous precision. And it seems to me that that has to be, we have to see why that precision comes along with this. And that precision has to be the result of the quantum gravity on the angular depth. Our quantum theory says time, and the quantum theory says time.

5:00 But one of the points I want to emphasise about this picture... The form of theory of space-time has to be time-asymmetric, because what it did to this point, it didn't do to that. It did something grossly asymmetrical. That's our theory of time-symmetry, and asymmetry doesn't reside in the U-part of form of theory, because the U-part of form of theory is time-symmetric. So it must reside in the R-part of form of theory, and the R-part of form of theory is time-asymmetric. And it's backwards in time if you know that it is perceived by the photocell, but if you don't perceive it by the photocell, you ask what's the probability that it's perceived by the lamp on top, or you find again a half, and you use quantum theory, and that has to be wrong, because it is perceived by the photocell. So there is this asymmetry in the half-half quantum theory, and so my view is quantum gravity has to do with it. It's not just quantum theory is going to modify gravity theory, gravity theory is going to modify quantum theory. In that particular example, it's pure gravity now. It used to be the case that people in general relativity were intimidated by people in quantum theory because they would say, look, we can predict the magnetic moment of the electron to 12 places a decimal. So now, in general relativity, we can get the motion of the binary pulsars in one part of the string to be the best in the context of the general mathematics, which I think we can now feel the confidence of at least being here in the space of time. It's at least as good as the best theory we have, maybe even the best theory we have now. So, perhaps the other one, Nadia, is that its quantum mechanics, that there's two discrepant procedures, U and R, should be united into one procedure. And the whole, the real theory that we're looking for, the real quantum gravity theory, which we've been working together, should involve both types of quantum theory together.

7:30 And when we make very tentative suggestions about how this might appear, I'll just show you a simple little experiment. We might have a particle which might go into a box of gas, but might not. Supposedly, that kind of experiment. So quantum mechanics we tend to consider the part that goes up here and the part that goes up there, the conserving weight. See that's what quantum theory does. It says there are different alternatives which might occur, but somehow have to coexist. And they coexist to compensate for the weight of the situation. But that's the way quantum theory works. So as long as it's all quantum, I thought you'd say, how's the life going here? How's it going out there? Well, what this real state is, is some combination of two things happening. Some complex amounts of weighting and dimension, some complex amounts of... So now it's going to go in. It starts hitting other particles. It disturbs all the other particles in the box eventually. And so now you have a linear superposition, according to quantum theory, of all these things being disturbed and all these things not being disturbed. And in this superposition, all the particles will be moved from one place to another. Now what I say is you've got to look at the gravitational field of those particles. Initially you think that's very small. And then you've got to look at the difference between these gravitational fields. Look at the difference field. Like that difference field, when you try to describe a quantum mechanically, if that difference field involves as many as one graviton, when that involves as much as one graviton, then the rules change. Instead of having a superposition of two alternatives, state plots into one or the other. That would require change in the structure of quantum theory, and that would require some nonlinear modification of the theory of mathematics, but that's the source of the problem. I'm afraid I have gone badly at the time, but let me just make one point. I want to go back to talking about brains, and whether brains might considerably be something of the future. For a picture that one has, it would be neurons, you see. Signals go on a quad equal to the axons, and then go on to the other side, and when they get to the other end, they join over to other hand drives and other neurons and synapses, and then the signal gets to a certain place, or it's a combination of this and that, or it becomes a V, or a VAR, or another. Perhaps there's a possibility of having the same sort of picture, and one has these connections between one and the next, or these are synapses.

10:00 Let me come back to something here. What I want to talk about, just before that, is something else, is to talk about, so I've changed the subject here, but I've had to turn it back in a moment, so this is, this is a subject covering a plane with tiles. You all know you can do it with regular hexagons where the triangles are, and a good many of you may know you can do it with kind of shapes like this, and so on, but the point is that the general problem of tiling a plane is an undecidable problem. If you're given a set of tiles, there's no algorithm for telling whether or not they will come into play. At least all these instances here, one knows they can't. For example, the tiling of these two types of blocks there. Showing you that, because there are actually substances which seem to have sorts of impossible symmetries between these things. As close as you got is that five-point symmetry. If you could have a crystal, it would seem like impossible five-point symmetry crystals. And that, if you look at the pictures, you see these crystallized objects with very, very accurate five-point symmetry.

12:30 And these things were believed to be impossible. They can only be achieved if you have Something like these tiles that I've just been showing you, whether exactly they belong to a mathematical dispute, but if they are like that, there seems good evidence to be at least close to it, when it comes to the following problem. If you actually play with these tiles, you can assemble regions like this, whether that's correct or not, and see whether they fit. If you're happy, then imagine these are atoms. When an atom comes along here, you have to decide which of these two. That's called an acai. Here, and that's perfectly all right, it could continue in principle forever from that point. Let's take that off, and put it on here instead, just like that. Now, that's all right too, that's good, out of the way. Suppose this stuff on here, and, unbeknownst to us, it can't be completed, the whole plane. You could go on filling out the plane, and you could quite happily dump it up there, but at this point, it goes to the back in such a different way. Either replace that one with that one, and then you're all right. But if the atoms are really doing something like this, how does this one know that it's not supposed to be moving? There's some non-local assembly. And the point of view, as it's controversial, there's a lot of arguing about these things. My way of doing this is that somehow you can't consider the assembly of these objects locally. What you can't consider then in the classical world is atoms coming along and sticking on to nice spots in the table. What you really should do in quantum mechanics is considering all the possible things that might happen all at once. So, that might happen, and the other one might happen, and so they both happen in linear superposition. Quantum mechanics is an integral of quantum mechanics. But nevertheless, you don't see something in a combination of this and something quite different here. You see one thing here. So at some stage, between the linear superposition of these alternatives and the final resolving of one or the other,

15:00 Well, you see, it's the borderline between the U procedure and the R procedure, so you don't understand it. There's something going on there, and my tentative suggestion is that in these connections, for instance, there are things known as dendritic spines. They can either grow or shrink, and they can improve or weaken these connections here. Now, there are various theories about why and when these things can happen. In fact, one of the important theories is memory, is that memory is carried out by change. But if memory is carried out by changing these connections, and after all, when I say memory, I mean long-term memory, then laying down long-term memories is something which can happen in a matter of seconds. These changes can grow. I'm trying to suggest that these changes can grow while something like what's happening in the present moment is going on. So you have to consider, at some level of operation, that these different alternatives will all seem proposed. And only in the legal level does it resolve itself like this one or the other. The new part of quantum mechanics, the R part, where one or the other has resolved that, involves some physics that we don't yet know. So what I'm saying is that that physics that we don't yet know, I'm suggesting is quantum gravity in some form, is non-algorithmic. There's something in that which can't be imitated by a material machine. I don't really know which way to start there. Not much of an exact class there, but the suggestion seems to be that that is basically something algorithmic. You don't have to worry about the real numbers and all that. It seems to be the algorithmic. And you have to look elsewhere for something which is not algorithmic. And I'm suggesting to be elsewhere. And I'm sure there's a lot which is speculative and there's a lot which is very speculative in all this. The theory spans the gap between U and R in quantum theory, and to try and find that theory is a real challenge. The suggestion here is that it's going to be a very difficult thing to find, but you should be bothered to listen to all the time we're going to be reading.