Secrets of the Old One
Professor Emeritus, Oxford University
Author, The Road to Reality
Author, The Emperor’s New Mind
Einstein referred to it as the secret of the old one. this is the theory of everything that explains all the phenomenon in the universe. Since the emergence of human consciousness, generations of thinkers, philosophers, and scientists have made enormous progress in understanding the world around us. The ancient Greeks were the first known for systematically study the nature of the world. In the late 17th century, Newton formed the three laws of motion, which underlie classical physics. Einstein, in the early 20th century formulated his general theory of relativity, describing motion at extreme speeds. In this era, quantum mechanics also emerged to describe physical behavior in the atomic and subatomic regimes.
It is now the early 21st century and we still do not have a consistent model that unifies quantum theory and general relativity and that also unifies the four fundamental forces of the universe. Superstring theory, the prevailing model for the past few decades, has not yielded a complete picture. Mathematical physicist and cosmologist Sir Roger Penrose joins us to articulate our understanding of the universe and talk about his new book. He is professor emeritus of Oxford University and his work has spanned many fields including physics, cosmology, and consciousness. Below is an edited interview between Frank Ling (FL) and Roger Penrose (RP):
FL: Professor Penrose, thank you for your joining us today.
RP: Hello. It’s a great pleasure to be back in the area.
FL: You’ve written a very engaging and insightful book, The Road to Reality: A Complete Guide to the Laws of the Universe. Could you tell us a little about it and what motivated you in writing it.
RP: Yes, well the book is meant to describe what is going on in basic physics today and what led up to that, in terms which are more technical than accounts you normally get in popular books. So, it was an attempt to describe things at a deeper level than you usually get access to without reading a full textbook. It’s not a textbook but it’s got more details than you normally find in popular books. I should perhaps explain the origin of the book, which might be of some interest to some people. Some years ago, I wrote a book called the Emperor’s New Mind and that book was describing a point of view I had about consciousness and why it was not something that comes about from complicated calculations. So we are not exactly computers. There’s something else going on and the question of what this something else was would depend on some detailed physics and so I needed chapters in that book, which describes the physics as it is understood today. Well anyway, this book was written and various people commented to me and they said perhaps I could use this book for a course Physics for Poets or whatever it is if it didn’t have all that contentious stuff about the mind in that. So I thought, well, that doesn’t sound too hard, all I’ll do is get out the scissor out and snip out all the bits, which have something to do with the mind. The trouble is that if I did that – and I actually didn’t do it – the whole book fell to pieces really because the whole driving force behind the book was this quest to find out what could it be that constitutes consciousness in the physical world as we know it or as we hope to know it in future. But without that driving force, the book didn’t hang together really so I had to think of some other basis for this. Initially I thought of a book half a long as the other and the other was around 450 pages or so, so it would be only a bit over 200 pages. But then, with this other motivation, which was to search for the laws that govern the universe at it’s deepest level. That meant I had to enter a lot of other things in the book and a lot of mathematics because I wanted to explain it at the same sort of detail I did in the Emperor’s New Mind or maybe a bit more. And this required describing a lot of mathematical ideas in not too much detail but to give the gist, basic feeling for what is going on and I made a list of all mathematical topics and I was rather horrified to see how many there were. And it was even worse in the sense because when I wrote the book, I kept realizing there were topics I hadn’t really covered and needed to put them in somewhere. So it made for a long book I’m afraid. But you have the advantage with the US printing; the paper is a little thinner so the whole book is not quite so big and it doesn’t weigh quite so much. And the paper is better quality so the pictures look better too.
FL: So let’s talk about physics. In string theory, the particles in the universe are generated by the vibration of loops of constructs known as strings. The mathematical framework for describing these loops requires multiple dimensions. One variation requires up to 26, while the conventional model relies on 10. In your twistor theory, you can do away will these extra dimensions. Could you explain that a little bit perhaps?
RP: Let me just backtrack a little bit. As you say, the way string theory requires all these extra dimensions and this comes from certain consistency requirements about how string should behave and so on. Now twistor theory is something quite different. It’s an approach to understanding how spacetime and quantum mechanics might fit together in some way. The basic theory in twistor theory is not to add extra dimensions. In fact, it is only crucially only three space dimensions and one time dimension. It’s the the number of dimensions we experience. But instead of adding extra dimensions, it’s a reformulation of spacetime as we understand it. So instead of thinking of points as being the fundamental entities, which is what you usually do when you think of space, spacetime, or events, instantaneous points, you think of entire light rays. It’s not quite that. Entire lights rays – you see if you made space, each of whose points represented an entire light ray, you’d find that space had five dimensions. Now, one of the basic driving forces behind twistor theory, which is fundamentally based on complex numbers. Complex numbers where you involve the square root of -1 into ordinary real numbers. they’ve been very useful in mathematics for many centuries. Only in the 20th century did they start to find a fundamental role to play in physics, namely, quantum mechanics. So suddenly you find these wonderful numbers that work so well in mathematics, but didn’t seem to have any role to play in the physical world now had a role to play in the physical world. Well twistor theory is trying to take that one step further, so you look for a role for these complex numbers, complex spaces, and so on to have a role in spacetime geometry. And what you find is that if you look at light rays instead of points, you find almost that the space of lightrays is a complex space. It can’t be quite be because the space of light rays is five dimensional and any complex space has to be an even number of dimensions cause dimension counts as two dimensions. So where is the extra dimension? Well what you find is that if you don’t think of light rays as sort of a path of a single point, you think of it as something spread out, which has a spin. Ordinary photons do have spin, they have a notion of helicity so they spin around their direction on motion. They can spin way or the other way and they can also have a different energy and what you find is if you incorporate these ideas into your photon, you get another dimension and you therefore get six dimensions. Miraculously, this six-dimensional space is a complex space so the idea of twistor theory is to take that complex space as your basic geometry and you try to work with that. Now it’s completely equivalent to the spacetime description. You can use one or you can use the other. If you take twistor space as the basic geometry, then you find it’s naturally complex and you do things, which are naturally complex and it drives you in a certain directions. That’s basically what twistor theory is about. Basically it’s a reformulation of geometry in a way that is more compatible with quantum mechanics. As it stands, it doesn’t change any physics. It’s just a different way of representing it. But I should say there is a bit of irony in this. In the book, I make the point that here we have string theory and here we have twistor theory and we don’t know if either one of them is the right approach to nature. But they both can’t both be because they are incompatible in the sense of having different number of space dimensions. The irony is that just a bit over a year ago, Edward Witten, the prime mover in modern string theory at Princeton has introduced many ingenious notions, which have pushed string theory forward in many ways. He wrote a paper on the web in December 2003 in which he combines the ideas of string theory and twistor theory. So the idea is that basically you don’t put your strings in these extra dimensions, which people have been doing up to this point. You put them in twistor space and twistor space is already there. It doesn’t need any spatial dimensions and shouldn’t need it because it’s already there. You can put the strings in that space and then what he also finds is that this enables you to much more easily obtain the sort of formula, which describes gluon scattering. High energy physics, strong interactions and things which you actually measure in accelerators. This is quite new in string theory and gives you results which are physically observable. So I find this development a very exciting one. Fortunately in the book I managed to catch this, not in any detail because it was at the last minute, but it is described in there. It affects the way one looks at the area.
FL: I’m just curious here. Could you also explain the essence of gauge theory?
RP: Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has. Herman Wiles introduced the idea of gauge theory. Maybe that came before the ideas of bundles, but the idea of a fiber bundle and a connection on a fiber bundle is basically what gauge theories use. I do describe this in the book. There is a chapter on these things, still in the mathematical part. You’re still doing mathematics at that stage. Let me describe Wiles’ original idea. Einstein introduced special relativity and there is a thing called the clock paradox or the twin paradox. It’s not really a paradox but if you have these two people, one who stays still on the Earth and one goes in a rocket ship to a distant star and comes back again. You find that the one who’s gone off and comes back has experienced less time back than the one back on Earth. But what you don’t find is that their clocks run at a different rate. You see, the one who has gone off and come back again, he brings his clock and it looks slow. Time has not moved as much, but it still ticks at the same rate as your clock does. But in Wiles’ theory, which he introduced as a generalization of Einstein’s theory, the idea was that you could incorporate electromagnetism as well as gravity. And Wiles’ idea was to say why don’t we generalize general relativity so instead of having clocks, which with the paradox could be slow but is not running slow, let’s suppose it might run slow. In fact, if you go though different routes in space to come back to the same point, you compare clocks and you find that one of them is actually running at a different rate from the other one. And if you introduce that idea, you get a formalism that incorporates equations just like Maxwell’s equations. Wiles’ idea was this was a unified field theory which includes electromagnetism. Well there is a minus and a plus to this. The minus was really Einstein pointed out this cannot be right and we know that this would mean particles would have different masses depending on what routes they take and it’s really incompatible with the facts, so that was a little bit of a disappointment to Wiles. But the upside to this was a little while later when the ideas of quantum mechanics came in, Wiles and other people changed their view as to what this theory was. It wasn’t a change in clock rates if you’d like or on the scale of the metric, which comes to the same thing, but it was a change in the phase of the quantum mechanical phase. So you have not a real number, which would be a stretch or squash in the time rate, but a complex parameter, which is a phase. You are going around the unit circle, multiplying by e to the i theta or something like this. With this idea, you could incorporate electromagnetism in a way, which is consistent. In fact, that is the way it is done now. This idea of Wiles’ is the first gauge theory. It was a way of representing Maxwell equations and how the electric fields, electromagnetic fields interact with particles in quantum mechanics. And it is exactly the way we do it. Now, that’s the first gauge theory. It’s called a gauge theory because the original Wiles idea was a gauge, you see it was a change in scale. But then it became a complex change and it’s not so appropriate to call it a gauge. But this is the same idea, but then this idea was generalized by Pauli and Schore and then Yang and Mills independently, a little bit later, but they were the ones who really developed the theory and people picked up on it. So this is called the Yang-Mills theory and it is found that this idea – in a more general form than Wiles had, which was just this phase – is a group bigger than that. It’s the basis of forces according to modern particle physics, both the weak interactions and the strong interactions are supposed to take place according to such a theory.
FL: In quantum theory, we are confronted with the paradox of Schodinger’s cat, where the cat is characterized as being in a superposition of dead or alive until it is observed. Now, you’ve collaborated with Stephen Hawkings. He is known for saying, “Everytime I hear about Schrodinger’s cat, I reach for my gun.” What does he mean there? Do you agree with him?
RP: It’s a pity he has to quote Goering on this. I believe the quote was not original with Herman Goering. It goes back before that, but I don’t like much that criticism. It’s not really a criticism. It’s just a feeling he doesn’t like the idea, but it doesn’t get you around the problem. Schrodinger pointed this problem out very clearly and I think he was absolutely right. He was saying if you apply my equation to something on the scale of a cat, you get this nonsense, which is this dead and alive cat at the same time. And he was saying you shouldn’t be using my equation, Schrodinger’s equation, to describe something like a cat. Something else has to come in. Now, he didn’t make any suggestions as to what this might mean, but I think he is right although all sorts of points of view are developed to try and accommodate Schrodinger’s cat one way or another. The main two are that somehow the environmental decoherence causes the state to get so complicated and mixed up with the environment that you have to change your procedures. None of these things really work if you follow them through. The second one is the many-world’s interpretation where we say the cat is there and these superimposed states and if somebody comes along and looks at it and that person now has superimposed versions one seeing the live cat and one seeing the dead cat. And they are in superimposition too and the argument is that somehow – you have to generous about that point of view here here – your conscious perceptions must perceive either the live cat of the dead cat and it is not really explained why. According to Schrodinger’s equation, you should be perceiving them both at the same time. That’s actually not what we perceive. It’s where you are driven if you don’t believe there shouldn’t be a change in quantum mechanics. You are driven to this many world’s view, but it doesn’t get you out of the problem. So what I’m saying is why don’t we think about changing Schrodinger’s equation at some level when masses become too big at the level that you might have to worry about Einstein’s general relativity. And that there will be a change in the structure of quantum mechanics at that level. Another way of saying this is what is quantum gravity? You see, most people think quantum gravity means you apply standard quantum to the structure of space-time and this means you have to do something different about space-time structure. Okay, I don’t have any qualms with that but what I worry about is why standard quantum mechanics at that level. Now, I can see why people when they do quantum gravity why they don’t change quantum mechanics, because if you change that, you’ve pretty much changed everything, so what do you do? So I can see that it doesn’t tell you where to go. Nevertheless, it what might what nature is doing and, I think there are good reasons to believe that that is what nature is doing and there are changes in the structure at that level. There are several different independent reasons to believing in this that are described in the book. A major part of the book is devoted to this issue with different aspects spread over several chapters.
FL: Steve Wolfram is famously known for developing Mathematica and he is also a pioneer for cellular automata, which lets you create complex patterns from simple algorithms. Do you see any promise or insight using these methodologies?
RP: Well, I think these are certainly interesting ideas, but I don’t myself believe there is any evidence these ideas are playing big roles in physics. So none of the standard physical theories can be thought of as cellular automata.
FL: Looking back, what is your most cherished epiphany?
RP: Well, you mean the thing I’m most proud of? I think it is twistor theory. It may not be the thing that most people know about that I’ve done, maybe non-periodic tiling’s or something. But twistor theory is the thing that I would like to be remembered for most, I suppose.
FL: What are your thoughts about Kant and Hegel? Hegel describes a very different road to reality–history as a dialectical series of events. You end the preface in your new book with a wonderfully wry statement about the need to study the forces that *really* shape the world, with ‘really’ in italics here. Can you share with us your thoughts about the human experience beyond physics?
RP: Ah, my goodness! You ask very difficult questions. Well, I don’t know if I can comment on Kant or Hegel because I’m no real philosopher in the sense of knowing what these people have said in any detail so let me not comment on that too much. This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it. Just in the end of the book, I do mention what you could regard as this other platonic absolutes. If you like what I’ve been concerned with, it is platonic absolute of truths and its particular form, that is mathematical truth, which is a sort of idealized form of truth. But I think it is a serious issue to wonder about the other platonic absolutes of say beauty and morality. I don’t think the case for them is as clear truth, but on the other hand, there does seem to be a connection between beauty and the search for these laws that govern the world and you certainly find that people are driven with this beauty as this sort of criterion or guide to discovery in this context. As for morality, well that’s all tied up with the question of consciousness. If you didn’t have any conscious beings in the world, there really wouldn’t be morality but with consciousness that you have it. So I think that the issue of how consciousness relates to the physical world is all tied up with morality but we have a lot to learn on that one.
FL: Finally, on a lighter note, let’s talk about pop culture. Reality and existence are recurring themes in movies and books. Question asked include who are we? What is real? Are you amused how these are treated in say for example in movies like the Matrix.
RP: Well I didn’t actually see the Matrix but I’ve seen other movies where with similar sorts of themes. I find it amusing and entertaining and I’ve always been a fan of science fiction. I used to read it a lot when I was younger. I like science fiction movies, but I think they are useful for giving us ideas and I think science fiction is very good at giving ideas. But on the other hand, you have to take it with suitable amount of salt. I certainly don’t believe that these things like Terminator or something coming from the future who is a mechanical entity. But they raise issues too, which are not trivial issues. Yeah, I enjoy them.
FL: Professor Penrose, thanks for joining us today. Thanks for your time.
RP: It’s a great pleasure. Thank you very much too.