Into the Impossible With Brian Keating - Sir Roger Penrose Faith, Fantasy, and the Big Questions in Modern Physics (#324)

Episode Date: June 22, 2023

Watch the video of Sir Roger's lecture here: https://youtu.be/smUYz9ti_bA Sir Roger Penrose, the celebrated English mathematician and physicist as well as author of numerous books, including The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics, joined the Clarke Center to share a talk titled "Fashion, Faith and Fantasy and the Big Questions in Modern Physics" based on his book of the same name. In his book Fashion, Faith and Fantasy and the Big Questions in Modern Physics, Roger Penrose argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today's researchers astray in three of the field's most important areas—string theory, quantum mechanics, and cosmology. * **String theory** is a branch of theoretical physics that attempts to unify all of the fundamental forces of nature in a single framework. However, string theory requires the existence of six extra hidden dimensions, which Penrose argues is not physically plausible. He also cautions that the fashionable nature of string theory can cloud our judgment of its plausibility. * **Quantum mechanics** is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. However, Penrose argues that quantum mechanics is based on a number of unproven assumptions, and that it may not be applicable to all physical systems. * **Cosmology** is the study of the origin, evolution, and eventual fate of the universe. Penrose argues that many of the current fantastical ideas about the origins of the universe cannot be true, but that an even wilder reality may lie behind them. Penrose concludes by arguing that fashion, faith, and fantasy should be replaced by physics: theories which, although they may be completely wrong, can at least be tested in the foreseeable future and discarded if they disagree with experiment or investigated further if not excluded by the results. The book has been praised by some physicists for its insights into the current state of physics, while others have criticized it for its negative tone and its lack of constructive proposals. Subscribe to the Jordan Harbinger Show for amazing content from Apple’s best podcast of 2018! https://www.jordanharbinger.com/podcasts  Please leave a rating and review: On Apple devices, click here, https://apple.co/39UaHlB On Spotify it’s here: https://spoti.fi/3vpfXok On Audible it’s here https://tinyurl.com/wtpvej9v  Find other ways to rate here: https://briankeating.com/podcast Support the podcast on Patreon https://www.patreon.com/drbriankeating  or become a Member on YouTube- https://www.youtube.com/channel/UCmXH_moPhfkqCk6S3b9RWuw/join Learn more about your ad choices. Visit megaphone.fm/adchoices

Welcome, listeners, to this replay episode of Into the Impossible. Left mostly unchanged, this is a recording of a lecture given by Nobel laureate Sir Roger Penrose at UC San Diego in 2017, hosted by the Arthur C. Clark Center for Human Imagination. It was introduced by the center's director, Eric Vary, and moderated by your host, Brian Keating. To get the most out of this, please watch the video. and subscribe on our YouTube channel at Dr. Brian Keating. That's DR. Brian Keating. You'll find other episodes with our friend Sir Roger, and you'll see his beautifully evocative hand-drawn illustrations. If you've been listening to this show for a while, you know that Sir Roger's 1989 masterwork, the Emperor's New Mind, was an inspiration for Professor Keating. Rogers' follow-up

to that book, Shadows of Mind, came out in 2017, and included, included new theories of consciousness. In this lecture, Sir Roger talks about his book, Fashion, Faith, and Fantasy, in the New Physics of the Universe. He discusses platonic ideals, quantum theory, cosmology, and the role of beauty in science. With metaphor and occasional whimsical twists,

Sir Roger makes some of the universe's most vexing scientific puzzles approachable as only he can. Please let us know what you think of Into the Impossible and share with us your suggestions and requests in the form of a review like this one from Apple Podcasts. From its YD92, great show, engaging conversations that I could listen to for hours, one of the best guest lists in podcasting, definitely recommend. And now, this extended episode of Into the Impossible with one of our greatest math and science models. Nobel laureate, Sir Roger Penrose, giving his UC San Diego lecture on fashion, faith, and fantasy, in the new physics of the universe.

Any sufficiently advanced technology is indistinguishable from magic. Open the bud bay doors, please, help. Good evening. My name is Dr. Eric Vieri. I am a professor in the Department of Neurosciences here at the University of California, San Diego. And far more fun for me is I'm also the Associate Director of the Arthur C. Clark Center for Human Imagination. It's my great pleasure to have my co-director of the Clark Center, Dr. Brian Keating, in the Department of Physics here, to introduce our guest speaker. So it's a great privilege. I am the token physicist here to introduce our esteemed guest speaker tonight, Sir Roger Penrose, who's the Emeritus Professor

at the Mathematical Institute of the University of Oxford. He's won many awards, and he's known for many, many things. I first encountered him at such an early age in high school that I was completely baffled by his work, which I have here, one of my favorite books of all time. I'm hoping to finish it someday. They, if you don't know, they sell Rogers books by the pound, okay? He makes a lot of money off these behemoths and they're wonderful. I was remarking today on how exquisite it is that he combines the two kind of hemispheres of the brain that were known for on the Arthur C. Clarke Center for Human Imagination. arts and sciences beautifully together where he synthesizes the works of art and as well as

new directions in science ranging from mathematical physics, pure math to cosmology to quantum physics. And he, although he's an emeritus professor, he is still actively engaged with research. And in fact, he's spearheading whole new directions in the study of consciousness, which is actually what brings him here in combination with this event that we're doing tonight. He's had tremendous influence. In addition to the work that he's done as an amateur, in my opinion, he's professional level artist, but he inspired the works of MC Escher,

or I guess you might say Escher, but his works on so-called Penrose tiling. It's just one of the many areas where you can see this influence that then extended to these beautiful pictures that I'm sure you've seen on your dorm room walls or your kids' dorm room walls with angels and demons interlocking in beautiful ways. That was deeply inspired by the work of Sir Roger Penrose.

I want to just quickly read a list of things that he does and he's known for. So the first thing is that he invented Twister. You guys ever play Twister? No, he didn't do that. He invented Twistor theory. He'd be far richer if he did. He invented the notion of spin networks, geometry, wild curvature hypothesis, penrose inequalities. As I said, Penrose tiling, which you can put on your Penrose stairs,

which he also invented, and the Penrose graphical notation, so many things, singularities of space and time relevant to black holes, Black holes, deeply influenced and collaborated and still collaborates with cosmologist ranging from Dennis Skiamma, who was an advisor to him many years ago. He's passed away and Stephen Hawking famously. And I think there was a cameo of you in the theory of everything, I believe. Not with you, but someone pretending to be you. And maybe we'll hear a little bit more about that tonight.

So I think I'm going to introduce Sir Roger. Afterwards, we're going to have a conversation, I believe, the two of us. Maybe field a couple of questions and hopefully it'll be a really interesting. enjoyable evening. So please join me in welcoming the fantastic and comparable Sir Roger Tenrose. This is the title of my recent book with the Princeton University Press. It's part of the title of this talk. I should explain something about the title because I think it, I, the Princeton University Press, it was in the early, I think something like 2005. I was supposed to give these lectures. And I think they woke me up too early in the morning

and something like that and wanted a title for the series of talks that they wanted me to give three talks, and I gave them this title here, and it was a bit rash because most of the, I think the three topics, at least two of them, the world experts were actually in Princeton. And it was a bit rash of me to talk in this way. I think they didn't come to my lectures.

that was all right. But anyway, let me start with the fashion. One of the ideas of string theory which people say is great merit is that it's a very beautiful theory, or the mathematics is very beautiful. And I should emphasize that the idea of beauty in scientific research goes way back. So in the Platonic days of Plato, there were these, perhaps a little before Plato, there were these four elements and the four known regular solids were supposed to represent the elements. So we had the tetrahedron, the first one there, which was fire, and then we had the octahedron which was air and the icosahedron, which was water and Earth was the cube.

And as far as I know, it's not just, well, I should say it illustrates one thing, is when somebody discovered another one, there were five, you see. You could always mold the physics into agreeing with the theory. So they had to think of another element, which was the ether or whatever made up the cosmos, which seemed to behave a bit differently from what went on on the earth. So that was all right. You could have another element. But so you could modify a theory.

If the theory produces something which wasn't part of the observations, you just modify your ideas and put the other one in. The only thing I know that this is good for, apart from being nice and elegant, is that if you take a cube, take two cubes, and those represent two sticks, two solid things, that's the cube, and then you cut them up and you can make two tetrahedron. Sorry, two tetrahedron, that's right, fire.

Take two sticks, rub them together, and you make fire, and you get an octahedron as well, and that's the smoke. So you could produce fire and smoke out of two cubes. But it's the only thing I know, which you can actually use this theory for, but never mind. It just shows that the idea of elegance doesn't tell you everything. It can be an important ingredient, but it's not everything. Okay, let me move onwards.

If I press the right button, I hope I'd press the right one this time. Here we go. Now, string theory certainly had its origins in a very elegant idea. I should explain what these pictures are. These are meant to be Feynman diagrams. and, well, if you're a particle physicist, time goes this way, from left to right, but if you're a relativist like me, time goes upwards. It doesn't make much difference, but you'll see that time is going upwards in this picture.

And the first one represents two particles coming together, making a third, and then that's splitting into two others. And here you have two particles and what's called exchanging a particle and so on. Now, these are different basic processes that particles can indulge in, that each of these diagrams represents a specific method, mathematical expression. And that's fine. It works beautifully well. The only slight problem is that this is meant to be quantum theory or quantum field theory. The only slight problem is when you have diagrams like this, which have closed loops, and it's the great strength, as you can talk about these things, that when you actually strictly use the rules for what these diagrams represent, you get infinity. Infinity isn't much use, but they have all sorts of tricks for getting rid of infinities. And that's part of the theory. It's full of these tricks for getting rid of infinities. But it was suggesting. I think Nambu was the main person made this suggestion, but if you imagine instead of these particles, see if we go back and think about the Feynman diagrams, you can think of the particle in time, as its history in time, would be represented by a line. So that's the particle that's moving in some way, and then it does something with some other particles, creates some others or annihilates them or so on. But then you have a problem because you get these infinities, and this comes about basically from the fact that you've got.

Well, you might say it's because you've got corners and things. Sorry, I've got the wrong way. And the idea of the string theory is now, instead of little having the particle being a point, and so its history is a line, the particle here, oh, I've done it wrong, the particle here is a loop, and so its history is a little pipe.

And where is the thing? I press to make the light go on. Oh, here we go. That's right. So you think of these pipes. It's a sort of plumbing, if you like. These pipes join together in various ways, and it gives you a kind of unity between all these diagrams,

because you can just stretch them and squash them, and they seem to be the same diagram. And then you have these things here, which are these things represent what are called remand surfaces. It's a very beautiful piece of mathematics, and that was one of the appeals of this scheme. It relates to a very beautiful piece of mathematics, And because of these things are nice, smooth pictures now, the claim is that you actually get rid of your infinities, and that's one of the great strengths.

So when I was first introduced to this idea by Leonard Suskin, I think it was, and I thought it was a wonderful idea. And indeed, I think it is an amazing idea with lots of potential. The only trouble was that it only worked, they discovered that it only worked when the number of space dimensions was 25. And to me, that was more or less the end of it. But I'll say a little bit more about that, because it wasn't the end of it for many people. Let me go on. You see, what do you do with all those extra dimensions?

Well, the idea was this, that the x, you see, we've only three dimensions of space instead of 25. So it's four dimensions of space time, and 26, the idea was altogether. So you have 22 dimensions, extra and where are they? Well the idea is they're sort of tied up in a little knot, which is so small that it doesn't bother you. And the picture is more or less here. This is the analogy of a hose pipe, and the hose pipe, no, I'm really not good at this.

I've got to press exactly in the right spot. My thumb doesn't do that. Here we are. There is the host pipe. So if you're a long way away from the hose pipe, it looks one dimensional because it's just, yeah, it's one dimensional. But if you get a up close and you look at the surface of the host pipe, you see it's got a two-dimensional surface. And that extra dimension is small in the sense of it's wrapped up into something small. And so the idea is that on the macroscopic scale, a large scale, it looks one dimensional, but really it's got extra dimensions. And the idea is that what you look at on the large scale is the four dimensions of space time, but when you look at it carefully, you see a lot of extra dimensions which wrap

up in this little small thing, and that you're supposed to get away with it for that reason. Now I had some problems with this because, well, I'll tell you the basic problem I had by relating this to something else which is useful for this talk. I want to say something, first of all, forget about the strings and everything. I just want to say something about big numbers. Well, ordinary arithmetic, first of all, when you multiply numbers together, you see, let's take A to the B, what does that mean? It means A times A times A times A, where the B is altogether, that's A to B to B.

B. Now you can do something a little bit more exotic by, say, A to the B to the C. Of course, you could read that two ways. You could be A to the B to the C, or A to the B to the C. Well, if it was just A to B to the C, that wouldn't do you any good because you can write it as A to B to B C. So it's A to the B to the C is what it really means. So that means if you have A times A times A that many times is it?

Well, it's B-dums, B-times, B-times, B-times, B-times, B-times, B-times, so that's what it is. Now, we have this sort of thing here. This is, if you just want to have 10 to the 100, now why am I saying 10 to the 100? Well, this is what's called a Google, and there was a mathematician's nephew, I think, who, I forget his name now, who liked to have a big number. He was quite young, about 10 or so, and suggested that here was a really big number, put down 100 zeros like that. I should say that this number does feature in the book

because it's, roughly speaking, the number of years that it takes for a black hole finally to evaporate away, according to Stephen Hawking's process, walking evaporation. So a Google year is about the length of time that the biggest of the black holes will live for. So, okay, so that's a useful number to know, maybe.

But here, you see, then this nephew decides that wasn't big enough, and he was a bigger number. So he and his uncle decides eventually that, well, a good thing would be a thing that they called a Googleplex, where the number of zeros was a Google. So you take a Google zeros, and this is 10 to the 10 to the 100. Now, that number is not all that big. I saw Ron Graham a minute ago, and he knows of numbers, which are absolutely stupendously larger than this, but let's not worry about this. For an ordinary person, that's a pretty big number.

It does feature, it's pretty small by comparison with something I want to say, which is actually the improbability of the universe in a certain sense. So let me come to that in a minute. You see, the point I really want to make here is if you have double exponents, A to B to the C, C is all important, and it doesn't matter what A is, more or less. And the thing I've got to hear as an example, this is the, if you like, the specialness of the Big Bang. I want to say that the Big Bang, as we see it,

is a very, very special one. And how special is it? Well, it's roughly speaking one part in 10 to the power, 10. I think I've got 10 to the power, 10 to the 124. Now, one thing I want to illustrate is that it doesn't really much matter whether that 10 is 10 or E or 2. If it's 2, you see the number at the top hardly changes at all. So it doesn't matter what the bottom number is much,

but the top number is all important. Okay, that's the main message I want to give you, except to say that this improbability of the universe, in terms of Google, I've forgotten this, Google multiplied by itself a million times or something like that. It's easy to see from here, but let me not say it because I can't see what I've written very well. go on. Okay, now I want to let these numbers become infinite. And some of you may know about

Cantor's theory of the infinite. I'm just showing you this picture to say you what it's not. Because this is one of the things about Cantor's infinite. You can take the number of natural numbers, 0, 1, 2, 3, 4, and that's the smallest of the infinite numbers. And one of the things that Cantor's theory says, if you have pairs of natural numbers, that's no bigger than the number of natural numbers. And you can see the pairs of them are represented by this array here, going off to infinity in both directions.

And I have these vertices of this lattice give you the pairs of natural numbers. Those are the coordinates. And the thing is, you can count them by going backwards and forwards like this in this zigzag fashion. And you can exhaust the whole lot just by counting individual numbers. So this is Cantor's argument for showing

that there are no more pairs of natural numbers than there are individual numbers. But you see, this kind of counting is not very continuous, because you can see if you want to go from this pair to this one, right up at the corner, you have to go all be down there and all the way back again. When they get really big, you have to go in a long way. And so the close numbers in the pairs,

or close numbers in the number that you're, so you're numbering the pairs here, and that's what I'll just say you count along this zigzag thing, the numbers can be far away even when the pairs are close to each other. So it's not very continuous in this sense. So what I want to say is something counting infinite numbers, but where it's really continuous numbers, and you want to make sure that it really is continuous. So this is the idea, and let's say what I'm talking about here, where you see, first of all, as opposed to the plane in the discrete case being

no more than in the straight line, this continuous counting. the plane has more numbers in it than the line, and a solid would have more numbers again. I'm going to call it infinity, or infinity to the one, is the number of numbers in a line, or a number of points in a line, continuous points in the line, A to the B, A squared, A to the two, is the number of points in a plane or a curved surface,

and A to the three is the number of points in a solid, and A to the N is in an n-dimensional space. You can make sense of all this. I don't want to say it's just waving of the hands. It really does make mathematical sense. But you can talk about these infinite numbers, and again, you find that the top exponent is all-important one. And that has a role to play in what I want to say about string theory,

so I'll come back to that. But first of all, let's just say what I mean here. You see, suppose I now count the number of functions, and this first picture here is supposed to be discrete functions. So when I say a function, you can think of each point at the bottom can take all the possible values upwards. And if these are discrete, and if it's A upwards,

and B this way, then the number of different graphs you could have is A to the B. That's just ordinary discrete things. But what I want to say, suppose it's continuous curves now, then I would write that, you see, the number going up this way, it's just a line as I've drawn it, but it might be a high dimensional space. So the number here, number of,

different graphs here would be a z of the v to the c and so on. So let me show you an illustration of this, which is, if I can make this thing work. So suppose you have magnetic fields or electric fields say in three space. And how many electric fields are there in three-dimensional space? Well, at each point you have the electric vector, so you have that little arrow there supposed to represent the electric vector, and you need three numbers to describe that vector. It has three components, and then then I have the three-dimensional space. So what is the number of different electric fields?

Well, it's infinity to the three to the infinity. Here, that's the line which I'm supposed to be indicating bottom line, that's right. So infinity to the three, infinity to the three, infinity to the three. Now, it's the top three. The trouble is these three is represent two things. It's the top one, it's the dimension of the space. And what I want to say is that if you have infinity to the A, infinity to the A, infinity to the B, to the, there's a C at the top, to the infinity to the C, the C is the all-important one.

And it doesn't matter much what the other ones are. So that's the point I want to make. And that's the dimension of the space. So it's the top three here, which is all important. Now why am I saying all this? You said this place was steps from the water. We just haven't found the steps yet. How much did we save?

Enough. Enough to get lost. Or you could book a stay with Hilton. Welcome to your oceanfront room. Just steps from the water. The Hilton sale is on now. Book on Hilton.com or the Hilton app and save up to 20% to get the stay you expected.

When you want savings, not surprises. It matters where you stay. Hilton, for the stay. I'm saying all this because if you have a space which has more dimensions than three, then the number of functions in that space is huge, absolutely huge, by comparison with the number of components. So you see, you might have a field which had a certain number of components,

but if it's in a large number of dimensions, it doesn't matter of hoot what the number of components is. It's the dimension of the space, which dominates everything. So this was a reason why I didn't like the idea of, more dimensions of space than we seem to see, because that means that the functions in that space, if it has more dimensions, will completely swamp what we see. And so why don't we have all these degrees of freedom, completely swamping everything flooding the whole space, and that would ruin the whole physics? Now, the sort of argument that people made here, and let me go ahead,

Well, here's the point. I should have given this slide here. You see, infinity of A is larger than infinity to the B. Or infinity to the A, I can't read what I've said, but you can read what it says there. If the B is, if the B is bigger than the D, then it doesn't matter what A and C are. So it's the top exponent, which is the important one. And that's the dimension of the space. And it doesn't matter who, how many parameters there are, how many degrees of freedom you're talking about,

If the space dimension is larger, it's going to swamp everything. That was the point that was making. But then people said, well, there's a history to this because there was a wonderful theory put forward by Kaluza, whether he was German or Polish, depends on he was born in a place, which is now part of, I forget which way around it was. It was part of Germany as now part of Poland or the other way around.

But anyway, you can take your pick. But he proposed this wonderful idea. Einstein has recently introduced his idea of space time, in which you had a curved space time, I should say, in which the gravitational field was encapsulated in the curvature of this space time. And the idea was, could you do something better than that? Because you don't want just gravity. You'd like to have electromagnetism.

And Kaluza had this wonderful idea that if you introduce an extra dimension, So the space time is five-dimensional, then you could incorporate electromagnetism and couples with gravity in exactly the right way. So that was really remarkable. So people say, well, five dimensions is good, why not higher than dimensions? But there's a key point here,

and that is that in Kaluza's theory, you needed to have a symmetry. So, oh, I pressed the wrong button again. I'm going to do that, I'm afraid. You need to have a symmetry, which is, You see, these, here is space time as we know it, so it's four-dimensional, and then we have these little curves, sitting over each point, you imagine another curve, so the whole thing is five-dimensional.

But because these curves have a symmetry, you can rotate it round in that extra dimension, that's not really an extra dimension. It's an extra dimension which doesn't carry any more information. So it's all right to have an extra dimension because all the function, the function on your space are down here, not up there. So that's fine. Klein changed the idea a little bit by making these extra dimensions small

in the way that string theory does, and I don't know whether he was allowing to have extra freedom in those dimensions or not. It's an example of what's a bundle. I don't think I should talk about this that'll take too much time. But it's an example of what's called the fiber bundle, and you want to say

that the freedom is in the bottom, not in the fibers. the same thing. What people used to say to me when I complain, they say, well, why don't you see all these extra dimensions, how do you keep them hidden? And the argument was as follows. Well, you can't excite those extra dimensions

because it would take too much energy. The amount of energy would take to excite the smallest mode of excitement of those extra degrees of freedom would be something like the energy in an artillery shell. And you've got to, they imagine you say you're doing this in a particle accelerator, and the accelerator has to give that particle that much energy that if it was in this room, it would be a disaster for us, I'm afraid.

But, so that was the, what's called the plank energy, and that, well, it's actually not quite that energy, but never mind about that energy, which would be ridiculously large, so the argument goes. Well, it would be ridiculous. And the point for me is that that's ridiculously large for an accelerator, yes. but that exciting that extra dimension is for the entire universe. So that amount of energy, an artillery shell, for the entire universe, is other chicken feed. And you consider the amount, you might imagine here, this is my picture, where we've got the Earth in its orbit around the Sun, and the amount of energy in the Earth's orbit around the Sun is million, million, I forget how many millions it is,

more than the energy you need to excite that extra dimension. So if that energy is spread out over the Earth's orbit, per se, it's a ridiculously tiny change to this. And so there's no reason whatsoever, as far as I can see, why you couldn't excite that extra dimension, and it would get excited. And it would also be disaster because you can choose singularity theorems that Stephen Hawking and I prove to show that it would not just excite that. it would be a catastrophic collapse in the extra dimensions, and so the whole thing would go to pieces. Well, anyway, that was my argument against all this, and I actually gave this argument in a conference just a little bit before I started lecturing in Princeton, I think it was

a year before, and it was one of Stephen Hawking's birthdays at conference. I was somewhere else first, and it was only the last talk of the conference, and I was a little bit worried that by giving this talk I might be tired and feathered because there were lots of experts in string theory in the audience. Although I escaped with being tired and feathered, the next day there was a meeting for a sort of more popular conference and I was wondering, well, what people would worry about my arguments. And Gabriella Veniziano, who is one of the originators of the ideas, the string theory, came

up to me and complained about something. this and said oh no no I didn't mean that it is it oh I see he said I like him a lot he's a very nice fellow and then Michael Green came up and he said well what's wrong you what you you haven't taken no no no and then Gabrielle said no no he did he didn't mean that he meant this and they start arguing each other so I snuck off and let them argue it was an interesting day because I sat down for lunch afterwards I sitting down at this table and Lenny Suskin came and sat down opposite me. He was the one who initially inspired me to think about

string theories as a nice idea. And he sat down, and I'm trying to get the wording right. It was something like this, pretty well word for word. You're completely right, of course, but totally misguided. And I wasn't never quite sure what he meant, but I think it was something like, don't worry about detailed mathematics. We know what we're doing and forget it. But I don't know if that's what he meant, but it was a curious comment, I thought. But anyway, it's very curious that I gave this lecture. It was written up. No comment, complaints of any kind, no suggestion that the argument was wrong, no suggestion of anything else about it, no saying, oh dear, yes, that's a problem. No absolute silence. And then also this has been true with this book.

I haven't had anybody complain about my argument in the, it's in the lectures of it. It's in the lectures Princeton, nobody complained about it, and I haven't yet have a string, maybe a string theory in Scheris and the audience who wants to complain to me about the argument, but it would be interesting. I'd like to have complaints actually because otherwise I have no idea what people think about it, but I can't see what's wrong with the argument myself. Anyway, let's move on. This talk is supposed to be not just complaints about current ideas, and that was a complaining

about string theory a bit. or at least the extra dimensions of string theory. And actually after my talk, which was on the fashion, the first talk in Princeton, a worried student came after me and said, what should I do? He was thinking of working on string theory, and he was a little bit discouraged by what I was saying. And he saying was there anything else he thought I might work on?

Well, this is, I didn't say Twister theory, which is what this is a picture of, which is what I was working on, partly because it's a bit too mathematical and I wasn't sure that... Well, it has also a problem which is still not totally resolved. And perhaps I... Well, let me say,

I... In my book, I do have a little section on this stuff. So, this is the picture from it. In fact, all the pictures I show you are from the book. This is a picture of Twister Theory, roughly speaking. And so just to tell you what it is, I'm not telling you what you used it for or anything here. But it's a nice mathematical picture.

Of course, that doesn't mean it's useful in physics, as I've emphasized before. But the picture on the left is meant to be space-time. So you think of this as a four-dimensional picture. Of course, I'm not drawing all the dimensions. And here's a point down here in space-time, or that's what we call an event. And this is the light cone of that event. That's all the light rays, which you see a light ray, here's a light ray up there. You think of a particle moving

along with the speed of light. So it will be a straight line in this picture, and the way you draw it is the speed of light as though it was one in the picture, so that the thing is that 45 degrees represents light ray. And what twisted theory does for you is the following. The light ray is to be represented by a single point in a new space, and the point over here, you think of all the light rays through that, and so this is this, you see, each light Suppose you're sitting at that point, you look out of the sky, all the photons coming in you for all directions, is the celestial sphere. And that celestial sphere has nice mathematical properties. It behaves like a complex, one-dimensional space.

I won't go into all this because it would take me too long. I just want to show you that there are things you can do using beautiful mathematics, and they seem to me to be much closer to the idea of physics because you have the right number of different. dimensions. You see, I should say that when people used to ask me why I didn't like higher dimensions, I had two reasons for not liking it. One was the public reason, which was more or less the reason I've given you, that these extra dimensions, you can't really hide them, and how do you hide all those extra degrees of freedom? And that was the main argument. The secret reason was that Twister theory didn't work very well in that number of dimensions. And Twister theory is very specifically designed. to be a three-space and one-time dimension. It really doesn't work properly with any other number of dimensions. You could start it, but it doesn't get very far. But it works beautifully if you've got three dimensions of space and one of time,

and then these ideas of complex geometry work very beautifully. I won't go into this. There are problems with it, which I think we do know how to solve, but it's a lot of things we don't know how to do. Let me not say any more about that. that. Okay, what's this? Well, you say I've talked about string theory and one of the complaints that people have, I haven't mentioned, but usually people who don't like string theory do mention, is that it doesn't make any predictions. And the usual argument is, oh, well,

you need all these artillery shell accelerators giving you an energy of that much to a particle before you're going to test anything. So they don't mind it being not testable because it's way beyond the scope of particle accelerators. Well, what about the next thing, which is the faith? Faith, I should say, is about quantum mechanics. Now, it's completely different, utterly different, in the sense that whereas string theory has absolutely no predictions, which are testable, may have untestable predictions,

because they're way beyond the scope of what we can experiment with these days. quantum mechanics have absolutely vast numbers of confirmations, predictions, and so on. So it's completely different kettle of fish. It is beautifully confirmed. And one of the initial types of experiment that people talk about is the two-slits experiment, very famous. Suppose you have a couple of slits there and a screen behind, and this is say an electron gun.

It fires electrons or some other particle, say, through the, they could be, they could be photons through the slits. Now let's, first of all I'm going to close one of the, put a little cover on one of the slits and it fires through the other. And you see what you get, this sort of scatter picture. The particles might get deflected as to go through the slit, but there is a sort of middle line which is the, where the particles mainly hit, but the scatter on one side of the other, but a little bit of a, you can see the indication of where the slit is.

If you close that slit and open the other one, you have a very similar pattern, but the pattern is moved over just a little bit because the slits in a different place, but it looks just about the same. So what happens when you open both slits? You might expect that you get this picture plus that picture, nothing of the sort. You get these bands where certain places where you find that the particle can't reach at all, other places where it's more likely to reach than the two pictures added together. So, P and Q, P is the example of where you, well, whichever it is, I can't see these things,

I'm sorry about that, you can see them. So you get places where you get these bands of enhanced, I mean, it makes no sense. You see if a particle behaves like a particle, why doesn't it just add the two pictures? Well, the thing is, this is the thing, it doesn't just behave like an ordinary classical particle, but it behaves in a certain sense like a wave, and the wave is what gives you the bands. So you see the particle behavior and the wave behavior both at once, because you get individual points on the screen, that's the particle behavior, and the wave behavior is the interference. So it's a very beautiful illustration of how quantum mechanics mixes these two ideas together,

and you have particles behaving as waves and waves as particles and so on. Now I'm not going to say too much about the way we work quantum mechanics, but I will say something about it. You see, what's the, what's this about? Well you see, according to quantum mechanics, it's not just true that individual particles could be two places at once. See, in order to explain the bands, you have to say the particle somehow fuels out both slits.

It doesn't just go through one slit or the other. It seems to go out through both slits at once. And that's, it interferes with itself, and some of the roots cancel and others enhance each other, but the particle has to be considered that it goes through two at once. And that is the way you do quantum mechanics. Crazy, absolutely crazy, but it works. Now this is an example. My humane version of Schroding is cat.

You see, it's the cat going to two slits, you see. So you could say why doesn't this work on a much bigger scale? So what am I doing here? This is the cat behaving like a particle going through two slits, sort of. And so what's the experiment here? Well, I've got up at the top here, I can press the right knob. Oh no, it's the wrong knob.

Sorry about that. I don't know why I'm so bad at this. Okay, you see here is what's called a, well there's a laser which emits a single particle. And then here we have a mirror, well, you might think of it as a half silver mirror or a beam smithers, it's called, that the photon goes through it and is reflected at the same time.

So it shares its existence between those two roots, And there it is. You see, particles couldn't be in two places at the same time. But if it goes through one, it activates a detector which opens that door. So if it goes down, it opens the A door. If it goes horizontally, it opens the B door. So if you follow Schrodinger's equation, Schroding's equation has this behavior of being linear. And that means that if A does something or B does something,

that the superposition of the two must be a superposition of the two. So the doors must be one door is open and the other door closed, superposed with the other door being open and the one door close. It's a bit hard to draw all that, but this is the, if the photon goes one way, it opens one door, the other's left closed,

it goes the other way around, and the poor cat sitting here encounters this super-zoned, it wants to get the food, which is down there. You can see the food in the room, and so the cat wants to go through the door to get to its food. But since the cat is, the doors are in a superposition in two places, the cat must be in the

superposition of two doors. Well, Schroding's version was a little bit less humane than this one. But the idea is that Schroding was demonstrating basically that his equation tells you nonsense. His equation tells you that a cat could be dead and alive at the same time

or in this case the cat could be going through both doors at once. And that's what his equation tells him. And so usually quantum mechanics, people say, well, no, you have to interpret it in some way, which means you've got to make a measurement or something. Well, why doesn't the cat itself make a measurement by noticing which door is open or something like that?

So you have a little bit of a problem. This is, I've been struggling with this for, ever since I, see, when I went to Cambridge as a graduate student, I went to lots of lectures which weren't anything to do with what I was supposed to be doing. One of them was a lecture, a brilliant lecture course by Bondi on general relativity, and that influenced me greatly. Another was a lecture on mathematical logic, which led me to Gerdl's theorem and worrying about consciousness and things like that.

And another lecture was a lecture by Dirac, the great quantum physicist, and his lecture was beautiful, completely different from Bondi's lectures was full of excitement and waving of hands and all this sort of thing. Bondi's was very precise and very elegantly done. And right at the beginning, he gave a demonstration illustrating the superposition principle. He said in quantum mechanics, see, a particle can be over here, or it can be over here, then it can be all these combinations have been here and here at the same time. That's the superposition principle. And then he broke a piece of it. of chalk and said, well, it's an illustration,

is this piece of chalk being in two places at once. And my mind wandered at that point. I don't know what I was thinking about. And then he had an explanation why the piece of chalk was not in the two places once. And I came back and I thought, what did he say? And I've worried about that ever since. He said something, the word energy, I think,

came in somewhere. But I couldn't see what energy had to do with it. So I've been worrying about that ever since. And I'll give you some bit of my worry. here, I think. I've forgotten what I've have on these slides, but I think that's one of them. Well, you see, here, what's this about? This is,

I should explain the origin of this picture. I was asked by the Hans Christian Anderson Society to give a talk. They were just coming up to the 200th anniversary of Hans Christian Anderson, and

for some reason they'd invited me to give a talk, and I was very puzzled by, this because what have I got to do with Hans Christian Anderson fair- I don't have any of the fairy tales. Well then I remembered of course that I'd written this book with the title the Emperor's New Mind and this of course was a play on the Emperor's New Clothes which was a famous Ants Christian Anderson's story which very much was influencing what I was talking about in the book. But I had to think of something else so I thought of well

I thought of the mermaid, you see. This is the little mermaid story. And in my lecture, I related it to quantum mechanics in various ways. Well, one of the ways was that the mermaid towards the end of the story, she is, I can't remember why, but the thing is, it's in the night. And when the sun comes up, the first ray of the sun, when it hits her, she dies. So I thought, well, why don't we save her by putting a mirror between that beam of the first ray of the sun, and so I get reflected up into the sky and she's fine.

But then of course, well, you know what I'm going to do, make it into a beam splitter or half silver mirror. And so the photon is split between going one way and the other, so she's in the superposition of being dead and alive. She's a Schrodinger's mermaid. So that was one of the uses of the mermaid in that lecture I gave, but it didn't feature in my book, I'm afraid, but it does feature here as an illustration of quantum mechanics. So this is an illustration of where quantum mechanics is done.

So this is really what it's about. The bottom part of the picture represents the quantum evolution, the Schroding equation, if you like. U stands for unitary evolution, and this is the Schroding equation. It's a deterministic evolution of the quantum state. So it chugs away and you could put it on a computer if you want to. It's rather hard to do, but you can put it on a computer. And that is the quantum world.

What's at the top? Well, that's the classical world. The letter C is being used here for classical world. And the quantum world, you see everything's all a bit of a mess and tangled up and unfamiliar creatures and who knows what's going on there and it's a very unfamiliar looking world. But then we have a more familiar world at the top where things are separated and so on. And what's the mermaid doing? Well, she, of course, is partly in the quantum world and partly in the classical world. She's magical, too. So she represents how somehow the classical behavior comes out of the quantum world. And the way that occurs in quantum theory is by another process, which is called the collapse of the wave function or the reduction of the quantum state, that's R in the picture, where suddenly this great entangled mess of things, you do what's called making a measurement, or something. something, what it means is a little obscure, because when you make a measurement, you've got to use a piece of apparatus.

If the quantum world is everything, then that piece of apparatus, which does the measurement, must also be part of the quantum world. And so why isn't it the bottom? Well, that's never explained. But there are all sorts of partial explanations which people give. I don't believe any of them. But something must happen, and I think something that happens is something mysterious like this. Mermaid, but not so mysterious as it won't be part of a future physics. But it's not part of the physics that we have today,

because the part of the physics we have today is either quantum or classical. If it's quantum, it belongs to this bottom world, and you get the superpositions of cats going different doors and so on. If it's the top world, you get going only one door, not the other, and that's what you see up here. And how does that work? Well, how we do quantum mechanics is illustrated more in this picture. This is the graph, well, I'm afraid I'm doing the quantum, the particle physicist's time going horizontally.

And the quantum state is represented by upwards. So the quantum state evolves according to Schrodinger's equation, or you, and then somehow a measurement gets made, and one of a number of sets of alternatives comes about, and then that evolves, and then one of them comes about, and then that evolves. That's the way we do quantum mechanics. It looks completely crazy, because, you know, there's not a systematic, system to the whole thing, but that's the way we do quantum mechanics. You plug it along with this unit's re-evolution and then suddenly you change your mind and you take it as representing

a quantum, sorry, probabilistic or a set of alternatives, one of which takes place. Some theories say, well, they all take place and you get all these many worlds happening all at once, but I want an explanation which describes the world we live in, and that's only one world. So you need something which really, this is an approximation to. It's crazy as a theory as it stands. It's the way we do quantum mechanics, but we want a new theory which really makes sense of it. So let me try and go ahead without making a mistake.

Now this here is a quote of illustration of what I think gives a reason for a new theory, or at least a reason for what it might be. And I'm trying to explain. I don't think I can explain all this here, but let me just show you. I like the picture because when I drew it, you see, I drew these pictures, and they were sent to the man who did the, looked at them and said whether it was good enough for the reproduction and so on. He was supposed to improve it, but I ended up by improving it myself because it was easier. But he thought it wasn't going to work very well because his picture at the top, you couldn't really very well see the dials and all that, and it needed a little bit of clarity. What I had to explain to him is this is a completely fictional piece of apparatus, doesn't you the damn thing?

So I just put it up there so you could imagine some complicated pieces of apparatus. And the point is it uses gravity in it. Somehow the Earth's gravitational field is incorporated in the quantum system you're describing. And the point I'm making here is there are two ways you can consider the Earth's gravitational field. One is the ordinary way that most physicists would use, and they do what's called putting a term in the Hamiltonian to represent the gravitational potential. If you don't know what that means, it doesn't matter.

But that's the standard way, and you can do that. But that's only Newtonian way. And we don't believe that the Newtonian way is the right way. We believe that the Einsteinian way is the right way. And the Einsteinian way is to regard the gravitational field is equivalent to an acceleration. So you imagine yourself falling in the gravitational field, and then your coordinates are this falling free field,

and then you do it this way. And you find almost the same answer, whichever way you do it. But there's a technical point, which I don't think I can explain. But the technical point is that the almost isn't exactly the same answer. It tells you it's fine if you've just got one gravitational field, but if you've got more than one gravitational field, you're in trouble. When I say you're in trouble, it means that you can't actually apply the quantum mechanics. You have to do something illegal according to the rules of quantum field theory.

Let me not go into any detail there. But it points out that if you have gravity in the picture, you've got to think of something else. Quantum mechanics doesn't work if you incorporate it with the Einstein equivalent principle, or Galilei or Einstein equivalent principle, which says that a uniform gravitational field is equivalent to an acceleration.

And that causes problems. And this is the picture as you're illustrating the source of problem you have. Here we have at the bottom a lump of material. I'm not having anything as complicated as a cat. It's a lump of a stone or a rock or something, which is put into a superposition of two locations. And then upwards we have now the picture of the space time.

Oh, I'm doing it on. Picture of the space time. And these are the different accelerations you have, you see. And the fact that the black one gives you the black curves of accelerations and the gray one is the gray curves. And the fact that they differ means that if you're trying to do the free fall argument, you're in trouble with trying to make them match.

And that, if you look at this carefully, you see, it leads to a conclusion which I've illustrated here. This is a picture of what happens to the space time. I'm afraid it's a little horrible looking picture, but never mind. That's the claim that what happens is something like this. You have here, it's really the picture I had a minute ago. with the two space times, but the two superposed space times have to come about because the rock gets moved into which superposition. And so initially the rock is in one place, and this is the curvature it introduces, and as time evolves, the rock moves into two positions, superposed, and so you have two space times which are superposed, and the thing is that this only lasts for a certain time which you can estimate,

but in terms of the energies involved in the displacement here. I won't go into the details there, but there is a well-defined formula which tells you how long it could last. And if there's a big displacement of mass down here, then it's a very short time. If there's a little displacement, it could be a long time. And it's such that the space-time displacement is what we could say,

one in what are called natural units. That's where you put Planck's constant equal to one, the speed of light equal to one, and the gravitational constant equal to one. You can just go away with doing all that. And if you do that, then one unit of time tells you how long it takes for this to take place. I wasn't saying anything about consciousness in my book, except a little bit when talking about this. But this does relate to the ideas which Stuart Hammeroff and I have been trying to develop. the what we call the orc-o-r theory, because it makes use of this idea where there is this choice that the universe seems to have to make. It does one thing or another, and that is the

choice which is made in this time. You can estimate from this picture. And the idea is these choices are taking part, not just one display, but there could be lots and lots of mass scattered, well not scattered is the wrong word, in an organized way over the brain in these microtubules is the idea, and the amount of you could calculate how much energy, how much mass there is displaced, and that gives you a time scale. And the idea is that a conscious experience comes about with this kind of choice that is made. So if there is a notion of free will, it's related to the choice that the universe seems to have to make whenever this measurement, whatever it is, self-measurement takes place. Okay, well, that's a little bit of speculation there, but we do have...

The point about this is that it is experimentally testable. Well, I mean what's experimentally testable, if you like, is the idea that I'm describing here and here that this reduction takes place in... in the time suggested. And this is a cartoon of an experiment which was being worked on for, I don't know, about a decade and a half or maybe two decades by now, primarily by the time. This is an idea that we developed together with some other people, that you have say there's a laser here emitting a single photon and this gets split into two directions.

And this one is kept in what's called a cavity, and it reflects backwards and forwards like this, probably about a million times. This one has a funny kind of cavity where it reflects against a little tiny mirror here, which is a little cube, which is about a tenth of the thickness of a human hair. And if it gets hit a million times by this photon, it will get displaced by something like the diameter of an atomic nucleus. But the idea is that that should be enough, if this scheme is right, within a period of seconds to minutes, depending on details, decay into being one or the other. So it's in a superposition of being hit by the photon, so it's displaced, and that's when the photon goes this way. If it goes the other way, it's not displaced, so that it's a superposition in one place and the other. And that superposition, the claim we make, is that can only last for a certain length of time. And if it becomes one or the other in that length of time, you try to bring it back and you'll see you've lost coherence.

And this detector up here, we'd see something. Whereas if it didn't lose coherence, it would go back into the laser and you wouldn't see it. So this would be a test for whether this is right or not. So it would be very interesting to see. there are other tests that have been suggested more recently for whether that will happen. Okay, cosmology. This is the last, this is the fantasy. Now, there's a little bit of a different story here because I was really aiming the chapter on, the third chapter, on inflationary cosmology.

Because the normal picture that we have today of cosmology is a bit like this thing here. time is now going up the picture in the way I like, and the time is going up this way, and this represents the entire universe. Well, you might ask, what's all the frilly stuff at the back? Well, that is just because I don't want to prejudice the issue as to whether the universe is open or closed.

It might go and do something at the back, or it might close up on itself. It doesn't matter much for what I want to say. It's easy to draw the picture if it's closed. Now, this is the history of the universe. Big Bang, it expands, slows down a bit, and then, oh dear, I'm really no good at this, slows down a bit, and then it does this exponential expansion, which got the Nobel Prize recently, the universe seems to be doing this accelerated expansion.

People refer to it as dark energy or something, but it seems to be consistent with the term that Einstein introduced into his theory of general relativity, initially in 1915, and then he introduced another term in 1917 for the wrong reason, because he wanted a static universe, and then he got worried because the universe was observed to be expanding, so he regarded as his greatest blunder to introduce this term. But his greatest, to say his that this term was this greatest blunder was actually a blunder because it actually seems to be true. So this is rather curious that Einstein introduced it for evidently the wrong reason,

but it seems to be the right theory. Okay, so that's fine, explains this picture beautifully, but what have I left out? I seem to have left out a major part of the theory which is what's called inflation. So they're supposed to be tucked.

Well, you see, I could, should say, Oh, dear, I'm really bad at it. Sorry. It's tucked into that little black point there. So inflation might be in the picture. You wouldn't tell because on the scale of this picture, it's pretty worth the scale, but the scale of this picture,

it would be tucked into that little black spot at the beginning. But the other reason it's not there is because I don't believe it. Well, I don't believe it. Originally I didn't believe it because it looked very artificial, and this is a picture, one of the reasons I feel it's artificial.

because, well, the main thing that inflation depends upon, at least the modern version, a thing called the Infloton field, which is a completely made-up field, and it's got a potential function which is represented in these different graphs. You have to draw the graph by hand, basically, so that it does what you want. And this is just a sample of different graphs

of what the Infloton field is supposed to do, and it shows you that nobody has a very clear idea, except that it's got to have a general picture like this, to do what you want it to do. But it's a made-up field, and there's no reason from particle physics to believe that that field is there. But it's supposed to do various things

which I didn't believe it did. One of them it was supposed to do was to iron out the universe, because the universe is very uniform. The early universe is very, very uniform, and inflation was supposed to make it smooth. Now, the pictures I've got here are various models of the universe,

not necessarily with inflation in them, but this is, oh dear, I really need a lesson on how to do work these machines. Here we have the Big Bang. Sort of if the universe was closed, it would look something like this, with expanding out and then it might collapse again and produce a great mess.

But the great mess isn't anything like the Big Bang. So this is a very general kind of singularity you get when it collapses, and this is what we have. Now, just reverse the time, and this is telling you why if you have inflation, it doesn't iron out this great mess. The great mess will be inflation or no inflation. You can see from this general argument that it won't iron it out. Okay, well, I shouldn't have wasted so much time on this, but let me go on.

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UN must be 21 to enter. Now, you see, there's another argument which worried me for a long time, which has to do with this thing called entropy. See, entropy is a very fundamental part of physics. It tells you a measure. if you like, of disorder. So the second law of thermodynamics is more or less a statement

that the entropy increases with time or the disorder increases with time, if you like, or it gets more and more random as time goes on. The top picture is a nice illustration showing you the sort of thing that happens if you have a gas in a box, you might have it cornered,

blocked off in the corner, you release it and it spreads out over the box. Now, the universe that we see there's a problem. Because if the second law of thermodynamics works way back in time to the Big Bang, where you see it's telling you that as you go into the future, the entropy goes up, the randomness goes up. So that means if you go into the past, the randomness goes down. So it must be very low entropy in the early universe. Now what we see was the main evidence for the existence of the Big Bang is this cosmic microwave background. And the cosmic microwave background is this wonderful spectrum.

I don't think I've got this picture here. The cosmic microwave background, one of the main features, it's got this curve, if you look at it, which, let me not explain it. It looks like this famous plank curve. And the point is it tells you that what you're looking at is maximum entropy. Now maximum entropy, you might say that's ridiculous because it should be minimum entropy. As you go back and back and back in time, it shouldn't be a maximum because it's gone down and down and down.

So why is it a maximum? Well, what you see seems to be a maximum. Well, the universe is expanding, so you might worry about that. But that's not the answer. It's clear you can give good reasons why it's not the answer. Let's not go into that, though. But the point is that what you're seeing is radiation from matter and radiation basically in equilibrium. together. So that is what's called a thermal state, that's the maximum entropy state of matter and radiation.

And that's what you see is radiation from that. What you're not seeing in that is the effects of gravity. However, there is another feature of the cosmic micro background, and that is it that the universe was extraordinarily uniform in the early days. Well, you see, that would be consistent with the top picture if it's high entropy, but you want low entropy. entropy. So the matter here in this picture doesn't do what you want. But if you imagine a box, galactic scale box, say, maybe this is just stars running around, then the tendency would be for them to clump because of gravity and eventually produce black hole. Now you see that goes in the opposite direction. So what you're seeing is great uniformity over the sky. In other as you see in combination of this and this.

Low entropy and gravity, high entropy and everything else. Now, this seems to me to be an extraordinary puzzle. And I never understand why cosmologists don't list as the big puzzles of cosmology. They have a nice list of things which are mysterious. And this is never mentioned. To me, it's one of the biggest mysteries. Why is gravity so differently treated for everything else? Everything else was maximum entropy, gravity was essentially minimal entropy.

And it's a huge imbalance. Now, the scheme, which I'm going to talk about, if I can push the right picture. Now, this is actually just a picture showing you what this imbalance does. You see, when the initially uniform matter starts to clump, it makes galaxies and it makes stars. and it makes stars, and it made the sun, and the sun is what we rely on for life. Now, you might say, what do we get from the sun? Do we get energy from the sun? Well, then you might think if the whole sky was the same temperature as the sun, that would be even better, but it wouldn't be any use to you at all, because it's not the energy that we come from the sun,

it's the low entropy in the energy we get from the sun. because the sun is out there and it's hot and you have a cold sky. The earth doesn't get energy from the sun. If it did, it would simply get water and after a few days it would completely intolerable. It would just, life would be impossible. But, of course, in the night, it all goes back again. But it all goes back again in low frequencies and it comes in high frequencies. It's yellow lies and infrared going back, basically.

and it's this large number of photons going up which take the entropy away and the low number which comes in, which comes in in a low entropy form. There's a point Schrodinger made a long time ago, but it's not very much appreciated apparently. But the point is that it's the clumpiness of the material which enables stars to get produced and black holes. I'm not going to explain the black hole so much. This is a space-time picture of a black hole, and the horizon is this little too.

which comes up in the singularity in the middle. But the point I want to make is these cone things. What are these cone things? These are light cones, and you have to imagine that the space-time has all these cone things drawn on it, which tells you what light would do if it were there. You don't have to have light there, but if it were there, it would follow the cones.

And I had a little bit of this with my twister picture. But what this represents, imagine a flash of light. The first picture is the flash of light in spatial terms. with three dimensions, there's spheres spreading out. But then I've got to throw away dimension over here. So what looks like a sphere here looks like a circle here. And so the cone represents what light would do if it were there. You have to imagine at every point in the space-time there is in the tangent space

a little cone like that. Okay, which tells you most of the structure of the space-time. It doesn't tell you quite the whole structure because it doesn't tell you how clocks behave. It tells you, if you know about general relativity, you know that there's a thing called the metric and the metric has 10 components and 9 of them, well really the ratios of the 10 components, tell you where that cone is. So that's almost all the information. The one missing piece is the behavior of clocks.

So you want to know how clocks behave and this is a cartoon showing you different clocks, identical clocks but moving with different speeds and the first thing. and the second tick of the clocks represented by these surfaces. Yeah. Okay. Now the clocks, we have extraordinary good clocks now. And the extraordinary precision of clocks depends basically the reason that it's so good in the sense, the ultimate reason, is because of the two most famous formulae of 20th century

physics. These are, well, one of them has to be Einstein's E equals M. the other one is Max Planck's E equals H Nu or HF, if you prefer F for frequency, but new is my frequency. And if you put the two together, you can just eliminate the energy from them. See, Einstein tells you that energy and mass are basically equivalent. Max Planck tells you that energy and frequency are equivalent. To put the two together, it tells you that mass and frequency equivalent.

So if you have a stable particle, and this is the history of a stable particle, It is a clock of extraordinary precision. So this is indicating it's an oscillator. It has a very, very high frequency. You can't use that directly, but the good clocks that we have depend on this idea, not directly here, but basically the same sort of idea is that you have this extraordinary precision because of the combination of these two very, very basic principles. So quantum mechanics gives you these very precise precise.

precise timing of clocks. Now, the converse of this, however, is that, let me go back to this first, that if you didn't have mass, suppose you just had photons, then they only travel along the cone, they are going and zipping along here, and the first tick is never even registered. So a photon doesn't feel the passage of time at all. Now why am I saying that? I can actually forget with my pictures what the next slide is, but have the Escher picture. What's that doing?

Yeah, I need that, I think. Let's come to this first, though. Imagine the very remote future. I should be giving you my universe picture, if you like. The very remote picture, and you wait for eternity. That's a long time. Well, you wait for, first of all the Google years for all the black holes. That's the boring time when you wait for a black hole to evaporate away.

That's really boring. But the very boring era was after that. There's nothing of any interest happening at all, that's why I can make out. But I was sitting and worrying about this in my office. Isn't that a dreadful fate for the universe? Just interminable boredom. That's the fate of the universe. But then I thought, well, who's going to be bored by this universe?

Well, not us, but it'll be photons mainly, and it's very hard to bore a photon. It's hard to bore a photon because, well, it's hard to bore a photon because, well, it's Stewart will tell us, it probably doesn't have any experiences. But that's not the point. The point is that the photon zips along doesn't even hit the first surface here. It doesn't even notice the passage of time at all. So it gets right out to infinity without noticing a thing. So that's the main point I want to make.

And it's the sort of thing I used to play around with decades and decades ago, squashing infinity down. And it was a good way of talking about radiation and black hole. and the energy they carry away and that sort of thing, which is very topical now. But this is a very nice Escher illustration of a particular type of geometry. It's called hyperbolic geometry,

particularly the type of geometry where you can see infinity. So here these fish are supposed to be, as far as they're concerned, the same right out to the edge. So the geometry they use is such that their scale is, you have to, they sort of rescale the geometry. so that they're the same right the way, as far as they're concerned, the universe is infinite, and even though they look to us as getting smaller towards the edge, as far as their geometry, they're the same size.

And it's what's called a conformal squashing down, and you can see that particularly in the eyes of the fish, because they're circles, and they remain circles right the way as close as the edge to the edges you can get. As far as these fish concerned, they like massive particles, if you like. This is infinity, the edge is infinity. But if they were like photons, they wouldn't care about the edge. And you can see that things which just respect the conformal geometry, that edge is just another place. So the photons go zipping earth, and they could be right out there.

So it's the same idea it's being used here now to talk about infinity of the universe. So what I'm going to do is to squash infinity down in the same kind of way. So what we have to imagine is that below this line, I'll tell you what that line is in the middle, in the minute, but below that is somebody's universe. Let's say our universe. And this is its remote future. And as far as the photons are concerned,

this is just another place like anywhere else. And so it comes uping along, it says, well, where am I supposed to go after that? So that's after infinity. The idea is it's go somewhere else. Now where does it go after infinity? Well, now let's think of us as the top part of the picture. Now, as you go back, this is supposed to be the Big Bang.

Now, I talked about the Big Bang being a very, very special state. And I used to have some complicated way of saying that. But my colleague Paul Todd, who was a student of mine a long time ago, had a much better way of saying it. He says, just take the conformal geometry, which means just take the light currents, forget about the scale, and the Big Bang, the idea would be, is a nice smooth surface, which you could theoretically extend to before, but why bother? It's not supposed to be real.

It's just a mathematical trick. So that was his idea. It's also physically a good idea because you could say, well, it's not just photons, as it was pretty well here, but you've got all sorts of particles, but they're very, very hot and energetic, and the closer you get to the Big Bang, the more and more energetic they get. So they're behaving like photons. So they have effectively no mass because their energy of motion completely swamps their mass. And so they're behaving as though they had no mass. And so again, they say, well, why wasn't there an existence for me before the Big Bang?

And that only works in these very special model, as I say, 10 to the 10 to the 124 special. These only very special models which seem to be what we seem to see. is the universe like that. So the idea is that the universe was of such a character that you could extend it conformity to something behind. And then the crazy thought here, now all this isn't so bad, it's not totally crazy. The totally crazy idea is my idea here,

which is to say, okay, this is drawn a little smaller, the picture I had of the universe before with its exponential expansion here. That's us. where we're down here somewhere, and you squash down infinity to make it a nice finite future boundary, like in the Escher picture. You stretch out the Big Bang, as Paul Todd suggests you do, and the crazy idea is that they match.

Well, our Big Bang was the continuation of somebody else's remote future. Our remote future will be the Big Bang of somebody else. I call this an hour-eon. That's the Eon before ours. This is the Eon that will come after ours. It's a little bit shades of the steady-state model where one used to seem to have to have this continual universe. Well, it's philosophically like the old steady-state model, but very different in detail. So this is supposed to have existed forever in this scheme, and there are various nice implications that the theory has, which are still being explored, and I think has a good chance of being run.

right, there are the main observations. I don't think there's anything more on this picture, so yes, there's nothing more. So let me just say, there is a, the question is, could you imagine signals? Oh dear. I'm not pressing, I've done the press to the more thing. Never mind. Could you get information through from one eon to the next? And the claim is, yes, you can.

And I thought, what is the most violent process that I could think of, which might get through. Well, I thought of collisions between supermassive black holes. Our galaxy has a black hole in its center which is about the mass of 4 million suns,

4 million times the mass of the sun. We are on a collision course with the Andromeda galaxy, which has a much bigger one, I forget, I think 40 times as big, I can't remember the figure. But when we collide, which we will do in a few thousand million years, not that long,

The black holes will maybe miss the first, they'll probably miss, but they may well feel each other out and eventually spiral into each other and there will be a one big whopping explosion and that signal will go right out and will be detected, detectable by people living in the eon beyond ours. So I'm saying that we could detect signals like that in the eon prior to ours. So it's a perfectly experimentally testable theory and the question is, is it right or not? Well, I'll leave it at that point. Thank you very much.

Ambition comes in all shapes and sizes. At First Citizens Bank, we roll with your goals because we're built for what you're building. Fit for your ambition for Citizens Bank. Sir Roger, that was quite thrilling to have you explain these concepts that have been so mystifying even to, professional card-carrying physicists and actually do it in person. And I was thinking, as you were talking about, eternity of Woody Allen's famous line, that eternity is a very long time, especially towards the end.

That's right. Well, it's not so long for a photon, tell you that. Right. Things are very laconic for photons. So, well, first I wanted to mention, and I forgot to do earlier tonight, that part of the reason that you're here is to, sort of kick off the celebration and this initiation of a new center that we're forming here in the Ohio, Penrose Institute, and one of the founding directors, James Tag

is over there in the front row, and we're hoping to form a collaboration with the Clark Center that will kind of spread the boundaries and increase the interactions, to use a physicist language, between the arts, the sciences, consciousness, the squishy sciences, the hard sciences, the life science. I was like when they say life sciences, because that means that physics must be a dead science. It's the opposite. So I wanted to take the opportunity. Thank you for being a part of that, and we're looking forward to many more fruitful collaborations and interactions to come. I wanted to start off tonight with a couple of questions that I have, because I have the microphone. And then I thought it might be fun because you mentioned today over

lunch earlier in the day that one of your desires when you wrote the Emperor's New Mind, which deeply inspired me, was that you'd get mail and letters from young people that got inspired into the line of work that you practice. And you said you were a little bit dismayed that you got a lot of letters, but they were from mostly old men. And I saw some nice young people in the crowd, and I thought it would be great to only take questions from young people tonight. How about that? But first we'll take one from a reasonably old person, although I'm a cosmologist, so everyone seems young to me. So you mentioned,

and I know that you actually have the fortune to study under Paul Dirac. And as a work of study lectures, yes. Yes, you attended his lectures. His breaking of chalk inspired you to daydream and then kind of reconnect later on. Here at the Arthur C. Clark Center for Human Imagination, we like to explore the connections between the arts and sciences. And one event that we did last month or two months ago now was with Ray Armand Trout, who's a professor of literature and poet and won the Pulitzer Prize in 2010. She's a member of the Clark Center Advisory Board as well.

And she and I had a great conversation. And we debated whether or not there's this relationship between science and the arts. And it's often, here we have, classes, and I'm sure there are such classes as physics for poets. And I debate, and she and I co-taught a class called Poetry for Physicists, and that was really fun to take that class and explore the commonality. But I remember mentioning in the first day of class that Dirac was famously anti-poetry, and

he would even say things like, you know, in science you attempt to explain the most complicated things with the simplest of languages, but with poetry, it's the exact opposite. And I wonder what are your musings? What similarities, differences do you see between these two different cultures as they've been described? Well, it's undoubtedly true that aesthetic judgments are important in science. Well, I would say important, particularly either in mathematics or in very basic science. You might have science complicated things which might not be obviously beautiful. and what, well, biology things are obviously very beautiful.

But I don't know. Certainly, let's speak only for the fundamental basic sciences. Then it's undoubtedly true that there is a deep beauty in the theory when you get it right. But I think it's dangerous to argue the other way, because people often do argue. Say, oh, my theory is so beautiful, it has to be true. Dirac himself said that. Yes, well, of course, he was rather more a better luck than most. I don't think we should call it luck.

But he certainly had a fantastic reputation in getting it right. Well, not quite always, but he had a very good, and certainly with the electron. There was some comment, wasn't it? But somebody asked him, when you were searching for the equation for the electron, how did you come across that beautiful equation for us? He said, well, I have a very keen sense of the beauty for a sense of the beautiful, and when I found my equation, I knew I was right. So something like that.

Of course, it's probably totally apocryph. That's right. That's right. But he did certainly value the beauty of the mathematics. I think it's undoubtedly true. If you get it right, I mean, the ideas of gauge theories. You see, it wasn't the idea, I mentioned the Kaluza-Kline model, But what really survived mainly was Herman Vial's idea.

He had a different way of thinking about how electromagnetism could be incorporated. And he had the idea, well, with Einstein's theory you can have a vector and move it round a loop, and it points in a slightly different direction when you've moved it around the loop. But his vials idea was if you have a little ruler, or the length of the vector if you like, if you like, and you move that ruler around a loop, it might be a different scale when you get round. And he showed that the equations, maximum's equations, could be incorporated, Max was electromagnetic equation incorporated in this idea. And then Einstein said, no, no, that doesn't work because

proton trache it round a loop and it'll be different from it. And it'll disagree with quantum mechanics and things like that. So, so Vial went away and said, oh dear, have something. what he said. But then he and the number of other physicists came up with the idea, okay, when quantum mechanics became established, and you say, well, you've got this phase, and this phase is somehow an unobservable thing, and you can't really tell. It go around a loop, and it can get rotated round, and that was the phase idea, and that's what we survives today. But of course the name gauge theory, which was, because originally it was a

gauge in the sense of how big it was. And it's a bit of a misnomer now because it's not really a gauge in that sense. But gauge theory is the foundation of all of the physical interactions, I would say except for gravity, which is a bit different. Well, some people say it's a gauge theory, but it's a different kind of theory. But the gauge theory is all the other interactions come from Herman Viles' beautiful idea. And fantastic. So a lot of times, you know, famous physicist Richard Feynman said, you know, anybody who tells you

they understand quantum mechanics is a liar. Sort of his polygraph test. What is it about quantum mechanics and cosmology to a certain degree as well that leads and lends itself to ribald speculation that kind of brings out? I'm sure you get your share of emails, and now you get emails instead of postal mail from people. Strangely enough, it's usually relativity. I've never understood that. You hardly ever get people complaining about quantum mechanics.

They complain about relativity all the time. Perhaps they don't understand it enough to complain about it. I'm not sure. But, no, it's completely crazy. You see, I have to blame a lot of the crazy theories people have now on quantum mechanics, because it is a completely crazy theory, but it works so beautifully well. But, you see, there is this thing about not understanding quantum mechanics,

and Niels Bohr has some statement. I forgot all it was now. Yeah, if you think you understand quantum mechanics. You haven't understood it, but I forget now what the question is. It's like spirit, right? It's an ex-spirits. But you see, there are two reasons, and I think there are two quite different reasons. And in one of my books I said there are two different kinds of mysteries.

They're the X mysteries and the Z mysteries, or the Z mysteries, as you prefer that. The X mysteries, well, the Z mysteries are the ones that you could sleep peacefully with. you see of snoring or something. They're the puzzle mysteries. They are puzzles. And for example, the entanglements, which are very mysterious things, you get, particles can be very far separated, and they still have share information in a certain sense between them, which cannot be explained in a classical way. So it's purely quantum mechanical, these entanglements. And you can do experiments on this, which seem to influence what the experiment does over there, but not in a way that you can send a signal. Very strange. And that's a puzzle mystery. It's not

inconsistent. It's just extremely puzzling. But then there are the X mysteries, and those are the ones that rear are, should be crossed off in the sense, you see. The paradox mysteries, so that's the X and paradox. And these, Schroding's cat, is a paradox, because it doesn't obey the Schrodinger equation. And you see the cat is either dead or alive, I've gone through one door or the other door. It's not in a superposition. And so it's really a paradox

with what we see that the world does. People have their ways of resolving it. Either you have to go into many worlds, and then you have to go into the many, it doesn't make sense in the idea. You've got to explain the world we actually see, not a whole host of things we don't see. And that's one thing which doesn't

explain it. Another thing which doesn't explain it, which is the conventional quantum mechanical view, is that somehow the system gets entangled with the environment. And then you say, well, you don't know what the environment's doing, so you do a trick which is sort of tracing over it. But it doesn't make sense if you look at it. It's what I call a double ontology shift. You have one ontological view. You say, well, the wave function describes the world, if you like. And then you say you've got to average over these different things, and then use another descriptor, which is called density matrix. And that allows you to do this averaging.

So you shift from the wave function, well, the state vector, to the density matrix. And then you do a little rotation of the density matrix, which is perfectly legitimate within the world of density matrices, and then you say you've diagonalized it, you say these numbers down the diagonal represent probabilities, and then you say, well, it's a probability to different states. that probability of different states is shifting back to the original ontology. And you've gone through and then back again, it's a complete cheat. You haven't got a consistent way of representing the world.

Continuously, so you have to make a jump and then a jump back. So it doesn't really work. So you've got to do something new. That's not quite fair on... There are models, and there are other models in the world I sort of hinted at here. certainly which preceded the one I was talking about, there's the DeBroy Bohn scheme. The trouble, one trouble with that, it's rather a mess, that's one trouble, but one trouble with it is it doesn't claim to have different results from quantum mechanics.

It just has a better ontology. I think it does have a better ontology, but it doesn't really do anything for you. These were these other schemes by Girardi and his collaborators, which were much better in a sense. So there were deviations from quantum mechanics which could in principle be detected, which a class of theory some were disproved. But I mean, this is a serious science. You can see, is that theory or is pure quantum mechanics still true? Do you have deviations from standard quantum mechanics? So the reason it doesn't make sense is it's not a consistent theory. We're trying to put it into a box that we can comprehend, but it doesn't mean it's a consistent.

So it's not our fault. It's the fault of the theory. Yeah. Yes. So I think I turned on it. So having touched upon deep space, cosmology, rocket science, I thought we'd turn to something simple like brain surgery and neuroscience. So like many of the audience members, I'm guessing, you arrived here tonight using trusting your life, essentially, to software, to a computer that you probably have in your pocket or your car has on its dashboard. a computer that guided you and you basically trusted it completely with your life and certainly

with being on time here tonight. I usually turn off the actual voice commands when I'm driving with my wife so I don't have two women yelling at me. But I wonder, you know, as computers get more powerful, as we build, as we're already building the fundamental cubits in my laboratory in here at UCSD and other groups around the world for quantum computers. And I wonder, you know, we hear about this logical progression where, you know, chess is very hard. And humans are very good at chess.

And then humans were beaten by computers at chess. Therefore, you know, computers are going to take over the world and software someday, especially even in the absence of advanced hardware, which we're developing here at UCSD, at Cal IT2 and other places. How is it in your mind? I mean, do you really envision that the ultimate, evolution of quantum mechanics will be to describe quantum computers as brains or vice versa or similar in a Turing sense that could not be distinguished. Well, you see, the view I have is actually not, you see, people complain and they say, well, you're putting, saying consciousness is a quantum process, and the brain is warm and messy, and how do you get quantum mechanics? Well, you see, I'm saying something worse than that. I'm saying it's not just quantum mechanics.

where quantum mechanics goes wrong. So we don't even know it goes wrong in this way because of experiments which have not yet achieved that level. So I'm hoping that they will show that it goes wrong in the way that it's claimed because the scheme that Stuart and I have developed in various ways depends on that scheme. So I think there's good reason to believe

that it does go wrong at that level, but we need better than reason to believe we need experimental evidence that that's correct. But this is, as I say, going beyond a quantum computer idea. It's saying a beyond quantum computer. So it's more exotic. Now, you see, my position is that quantum... See, there's different things here.

I'm saying that consciousness is something which is not a computer action. It's not the inaction of an algorithm. It's something beyond an algorithm, which enables you to achieve things which pure... algorithms don't achieve. And we know that there are, mathematically, we know there are limitations. That's absolutely established mathematics.

And these limitations are well understood. But whether the brain does something difference is another question. And I believe that you can make good arguments that it does do something different from pure computation. And if it's a quantum computer, it doesn't do that. You see, quantum computers just do computation. They may do it faster. There are certain types of computation that they should do

faster. It's a little bit limited at the moment what they seem to be able to do. It's not really like an ordinary computer where you can program it in all sorts of different ways, and it does fantastic different kinds of things. Whereas a quantum computer, it's just a very limited number of things that we know it can do in principle better than an ordinary computer. But maybe that's a temporary stage. But it's still a very only doing computations faster or more bigger computations or something more powerful. So there's not a qualitative difference in what they can do. The claim is that if you could have a beyond quantum computer,

I think there's an name that people have given to that, that incorporated whatever it does, whatever the world does when it reduces the state, and that's what Stewart and my ideas suggest would have to be the case. Yeah, that would be, it could. But you see, it's not on the spectrum of what can be achieved. You see people talk about 10 years, 20 years, even 30 or 40 years, but this is something which we have no idea how you would do at present time.

Yeah. Very good. So I'd like to take maybe two questions from audience members under the age of seven. No, I'm just kidding. us. Maybe preferably a young man and a young lady could ask a question, that would be fantastic. Is there a volunteer in the back? Young man? Young man? Okay. Let me see. None of my students qualify as young. Okay. Well, we should start with the youngest possible. Are there any questions up in the front? I see some very angelic young faces here. Here's one. Okay. Is your chance to interact with physics royalty?

Hi, thank you for speaking today. This has been really interesting, but I had a question about your cosmological theory concerning the aeons and the inevitable big bangs. So if I understand correctly what you're saying is that in our distant future, there's going to be a big bang, and then in that universe's distant future, there will be one. But if the rarity of a big bang exists, then are you saying that it's a rarity that is inevitable or that the first big bang was just a very rare occurrence and that now it will no longer be a rare occurrence? I did quite catch the question. I can tell you what I'm not sure that I caught exactly what the question was. I'm sorry.

Oh, sorry. Yes. Was there a first big bang? Oh, first big bang. When the scheme I have, they go on indefinitely. So there wasn't a first one. It's a bit like the steady state model in that sense that the universe was already there.

I worried about this because I once gave a talk in the Vatican, and I was worried that this model would not be viewed with favor because the origin of the universe was supposed to have been at a certain stage. But they took one I regard as the correct. attitude from their perspective, namely that the creation of the universe was the creation of the entire thing all there, boom. And so not bang, but boom, I suppose. This whole thing was this infinite sequence of things, yes. But that's, it doesn't have to be like that. It could be something where there was a really a beginning

one. And so how would one tell that? I had no idea. You need a good theory, which really pins it down much more than I'm able to at the moment. So if the theory really demands that it does go on forever, and that would be the way I view it, then that would be it. Yes, there is no original one. It was there forever. Okay, great. Maybe one more question. There's a very young man in the front. Let me make sure this is on. Here you go.

A copy. Thank you. So my question on consciousness is that I, in thinking about data and what we see and what can test and demonstrate on consciousness, when we see, for example, not religious near-death experiences, but they die on the table, they go to another room, they report things, sometimes miles away. In theory, what would you say, could explain this? You're thinking about sort of ESP, you mean?

Yes. Yes. Well, I'm not a fan of this. that idea, partly because, well, you see, I mean, who knows. But I suppose the idea is some sort of quantum entanglement between states, between brains and different rooms. I don't know how you'd get that from one to the other. That's the problem.

I mean, it's hard enough in a single brain to see how you can get the kind of entangled states that you need for this scheme. You certainly need something which would cover large areas of the brain so that the quantum state, if you like, isn't just within a single neuron. It would have to be extending across several, maybe loads and loads of neurons altogether.

So there is some kind of, not exactly EPR, that extrasensory perception is that. Extrasensory, what's the R, that? Anyway, the thing is it's within one brain. But if it's from one brain to another, I really have no idea how you could conceivably get the entanglement established. It's hard enough in a single brain

to see how that's going to work. So I just have, I think it's a pretty long shot. Thank you. I'm afraid. So part of the reason I wanted young people only is so that I can get first dibs on their applications to come to UCSD. Thank you, young people, for your questions. I'm sure there's many more.

We'd like to thank Sir Roger Penrose for coming tonight. Any sufficiently advanced technology is indistinguishable from magic. Thanks for listening. Keep in touch and inspired by signing up from Professor Keating's Monday magic email at brynekeeting.com slash list. And if you have a dot edu domain, will send you an artifact older than the earth, forged in the fire of an exploding star, in the form of an authentic meteorite fragment.

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