In Our Time - Grand Unified Theory

Episode Date: February 24, 2000

Melvyn Bragg examines 20th century physics’ quest for the ultimate theory of everything. Einstein left us with his theory of General Relativity, which explained how gravity works on the scale of stars, galaxies, and the universe itself and Schroedinger left us with the equation that explained the mechanics of the tiny quantum realm. Both theories work to wonderful effect in their own worlds, but (and this is the sticking point) gravity is strangely absent from the quantum realm and planets behave nothing like particles. The enigma for scientists throughout most of the last century is that, as they are currently formulated, general relativity and quantum mechanics cannot both be right. The history of twentieth century physics has been a struggle to find a way to unite them, to find what has become the holy grail of modern physics: The Grand Unified Theory. With Brian Greene, Professor of Physics and Mathematics, Columbia University and Cornell University; Sir Martin Rees, Astronomer Royal and Royal Society Research Professor in Astronomy and Physics at Cambridge University.

Thanks for downloading the In Our Time podcast. For more details about In Our Time and for our terms of use, please go to BBC.co.com.uk forward slash radio 4. I hope you enjoy the program. Hello, Einstein left us with his theory of general relativity, which explained how gravity works on the scale of stars, galaxies and the universe itself. And Schrodinger left us with the equation that explained the mechanics of the tiny quantum realm. Both theories work to wonderful effect in their own worlds.

and this is the sticking point, gravity is strangely absent from the quantum realm, and planets behave nothing like particles. The enigma for scientists throughout most of the last century is that, as they're currently formulated, general relativity in quantum mechanics cannot both be right. The history of 20th century physics has been a struggle to find a way to unite them,

to find what has become the Holy Grail of modern physics, the grand unified theory. With me to discuss the dilemma of modern physics and the quest for its solution is Brian Green, Professor of Mathematics and Physics at Columbia University and author of The Elegant Universe, Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory.

I'm also joined by the Astronomer Royal, Professor Sir Martin Rees, whose work just six numbers also tackles this problem. Brian Green, can we begin by explaining why Einstein's theory of general relativity can't be incorporated into the current understanding of quantum mechanics?

Sure, the basic idea in Einstein's theory of gravity, general relativity, Strangely enough is that the fabric of space itself is connected with the force of gravity. It's kind of a hard idea to imagine, but it's as though the fabric of space bends and warps, and in that way communicates gravity. The only thing we need to know, though, is that the curves in space from his theory are viewed as gentle, gentle curving geometry. But at the other end of the spectrum in the quantum realm, we learn that microscopically the universe is a jittery,

frenzy, turbulent arena, very different from the gentleness of Einstein's theory. And it's that jitteriness of quantum theory versus the gentleness of general relativity, which makes it so hard to unite them together. In your first sentence, you said, the fabric of the universe. Could you tell people what you mean by the fabric of the universe? I don't know. Sure, it's one of the more elusive ideas of modern physics, but it's very powerful one. It's as if we are all immersed within an environment, the fabric of space. It's the stuff around us. You can't really grab it or hold onto it, but you can feel it. Because right now, each of us is being pulled by gravity. We feel that, each of one of us. And according to Einstein, it warps in the fabric

of space, which cause us to feel gravity. So you, me, everybody else right now, we are sliding down an indentation in the fabric of space caused by the presence of the Earth. We are all moving, in a sense, under that force right now. And why is that so distinctive from quantum Why is that relationship so far away from the way in which you understand the world at the tiniest level? One would presume that from the tiniest comes the greatest, from the small comes the big, from the detail comes the general and so on. But what you're saying, I mean, my goodness, am I being banal? Never mind, here we go. What you're saying is, right, there's this huge theory which gently warps the varieg of the universe.

And then it is, but it is built on the particles, the quarks and nothing at the bottom, which, a theory which has got nothing to do with the huge theory. And so ordinary judges would say, well, why not the building blocks lead to the building? Well, that's exactly what's been motivating us for 50 years. We hold that same intuition that the big stuff should be built up from the small stuff, and therefore the two theories that have been developed of the small stuff, quantum theory and the big stuff general relativity, should fit together. They should smoothly move from one to the other, but as they're currently formatted,

they don't do that. That's been the driving force. Now, why don't they fit together? Well, we think it's because when you formulate quantum theory, it's a very different language. It's a very different philosophical orientation to how the universe is put together. And that has been part of what we need to overcome in stitching these two theories together. But when we talk about missing physics, we mean we've got the little, we've got the big, we need something in between to link them together. We need a bridge between those. Martin Rees, how do you see that? Well, we do need the bridge, but we've got on fairly well in most of science without the bridge,

and the reason for that is that normally we don't have to worry about quantum theory, that's the microphysics and gravity at the same time. In the case of ordinary atoms and molecules, we have to worry about all the counterintuitive effects that we've learnt about since the 1920s called quantum theory, but on the scale of single atoms, gravity is quite unimportant. On the other hand, when we get to the astronomical realm, the Earth, planets, stars, etc., gravity is the dominant force.

It's what's holding us down on the Earth. But in large objects like planets, gravity is dominant and the counterintuitive features of the micro-world, the fact that on the very small scale we can't localize things, we have this intrinsic uncertainty, those effects are not important on something as big as a planet. And therefore, it's only in extreme situations that we actually need to confront

this unification and those extreme situations come first of all right at the beginning of the universe when we believe everything in the universe was squeezed to the size of an atom as it were so we clearly have to worry then about gravity and so we won't understand the

real beginning of the universe until we have a theory that can cope with both gravity and quantum theory and also there are other exotic situations and of course as Brown Green said we won't understand really what space is like unless we can understand its structure and why it has the effect of transmitting gravitational forces, as it were.

Don't you find it intellectually annoying, though, to put it at its very slightest, that these two things can't be connected? I mean, in your work, you find yourself able to do your work without any reference, from one theory without any reference at all to the other, you don't think that perhaps the other might be having some effect that you haven't yet, did I want to say it, imagined or thought? Well, certainly we'll get a deeper insight when we have this complete theory, but I think it's important to realize that most of science gets along on the base of its set of concepts

that don't involve all these deep mysteries. Ordinary atomic physics and chemistry and certainly biology proceed independent of all this. So it's only some kinds of science which actually depend on having these new theories. But conceptually, of course, these theories are crucially important because, in a sense, they would be the next step in the quest to understand the basic stuff the world is made of that goes back to the Greeks. We have understood for at least this century that everything is made of atoms. We now understand the structure inside those atoms.

But the next step, of course, is to try and unify all the forces, to connect the forces that govern the micro-world of atoms. These are the forces of electricity, the forces that hold atomic nuclei together, which we do understand to some extent, and to link those with the force. of gravity, which is what we feel here on Earth. And that is the challenge which Brown-Green is addressing. I'm coming back to Brown-Green in one moment,

but as I understand it, Heisenberg's uncertainty principle is one of the most profound aspects of quantum mechanics. Now, can you just say how it affects quantum mechanics and why it has no place in the work you're doing in astronomy? Oh, it has a very big place in my world because the whole nature of atoms depends crucially on the fact that atoms don't obey the ordinary billiard ball equations that Newton taught us and to understand everything about atoms and how they stick together to make molecules, planets and stars.

We certainly need to incorporate quantum theory, and indeed most of 20th century science and technology depends on the fact that on the scale of atoms everything behaves in this very spooky way, as it were, where you can't say simultaneously exactly where an electron is and exactly how it's moving. I expressed myself badly because what I meant to say was that what we know about that, does that affect your work on positioning the planets, for instance?

Well, when we are talking about the gross features of the universe, the planets and the stars, etc., then we are concerned with gravity and Einstein's theory of gravity is good enough for all these situations. The planets and the stars move in their courses through space according to the laws of Einstein's theory, which in fact in these contexts aren't too different from what Newton taught us 300 years ago, and because the plans are so big,

the sort of jitter or fuzziness in their positions which stems from the Heisenberg Uncertainty principle is trivially small, because the bigger an object is, the more firmly localized it is. So it's only when you get down to the very small that you have to worry about this fuzziness, or in the case of the universe, when you get back to the incredibly high densities,

which prevailed at the beginning when the entire universe, as it were, was squeezed so small that a quantum fluctuation could shake the whole thing. So we've reiterated that what you said at the beginning, that you can effectively get on with the work you're doing with one theory and without the other. Brian Green, more than once, Martin Rees, pointed us towards the Big Bang, which as being both massive and tiny, supposedly, you're going to tell us,

containing all matter in the universe yet compressed into something incredibly small. Is it calculations in this field that are the driving force behind the quest for the grand unified theory? Certainly, the deepest questions that a unified theory such as string theory faces is trying to describe extreme realms of the universe where you need both the laws of gravity and the laws of quantum theory. And those are realms that are huge and heavy, but also tiny from the point of view of size. So the Big Bang, when everything in the universe is crushed together to incredibly small size, it's heavy, but it's small. Black holes, another realm where a lot of materials crushed to incredibly small size. Again, it's very massive, but very tiny. Those are the

realms where these unified theories come into play, because you need the ideas of both quantum theory and gravity, namely general relativity. So what do you know about the big, bang in terms that would make sense to me and I hope to people listening, that gives you hope that these two theories will come together. You've described it in general terms. What more particularly? Well, the Big Bang is an area of very active research today, and string theory by no means has resolved many of the puzzles surrounding the Big Bang. But Black Hole, the other example I gave, perhaps better illustrate some of the power of these ideas, because in the last few years, string theory has been able to resolve an idea that was initially put forward by Stephen Hawking in the 1970s having

to do with black holes. He discovered an interesting fact. Black holes, it turns out, embody a certain amount of disorder, or the more technical term is entropy. But nobody could figure out where the disorder in a black hole came from. Finally, string theory, using the new ideas of the last few years, has been able to very accurately describe where the disorder in a black hole is and came out with a numerical answer that agrees exactly with what Stephen Hawking had predicted. So it's a very powerful confirmation that these ideas are making contact with real physics. Could you tell us, is it possible to tell us? I mean, some things aren't possible to say in a conversation, but is it possible to tell us what string theory is?

Sure. I think the basic idea of string theory can be described quickly in a nutshell, as Martin Reese was saying, we have for thousands of years asked a simple question, what is the stuff of the universe made of, namely if you take any piece of material, wood, iron, anything, slice it in half, slice that piece in half again, and keep on cutting, what's the smallest ingredient that you'll come upon? And indeed, in our century, we've learned about atoms, but we know atoms are not the end of the line because they're made of smaller things. They can be split. They have little electrons that swarm around a central nucleus, and it can be split because the nucleus itself has neutrons and protons. And there, not the end of the line either.

It's somewhat like a sequence of Russian dolls. Inside neutrons and protons are smaller particles. discovered in the late 60s, known as quarks. What string theory does, it comes along and says there's one more layer of structure. Deep inside an electron, deep inside a cork, deep inside any particle, in fact, is a little tiny loop of energy, it's a little filament of energy, vibrating to and fro. And the key idea is that just like the string on a cello or a violin can vibrate in different patterns, which our ears sense is different musical notes. The little strings and string theory also can vibrate in different patterns,

but we don't hear them as different notes. Rather, we see them as a different particles in the world around us. So using the metaphor, an electron is a string vibrating like an A-sharp or a cork is like a string vibrating as a C-flat or something of that sort. So that is the way in which we can think of all of the rich material in the world around us being generated from one fundamental vibrating ingredient. How do you see, no, understand, how do you get your, I mean, hands on that, worn vital, can you see it?

Or is it just, is it an active imagination? At the moment it's an active theorizing, so it's imagination, but bolstered by the quantitative ideas that we're able to develop surrounding the idea. But the reason we can't see it yet is because the

strings are really tiny, so just to give you a sense, they're about, well, numerically a billionth of a billionth the size of an atom, so they're tiny, but an analogy, I think, gets the idea across better. If you were to take, say, a single atom and magnify it to be as big as the entire known universe, then a little string and string theory would magnify roughly to the size of an average building of maybe 10 stories.

So a 10-story building is to the entire universe as a little string is to an atom. So that's why they're so difficult to see directly because it's way beyond our technology to see something that small. But you're absolutely sure though there, are you? Absolutely sure, certainly not. We won't It won't be absolutely certain until there's experimental proof of these ideas. But the last 10, 15 years have convinced us that this theory can solve problems, which could not be addressed in any other method. And just going back to the somewhat philosophical side, I think each of us, I think, has a gut sense

that the universe cannot really be described by a patchwork of two good theories, each of which is incompatible with the other. The universe exists. It's a single place. It should be a single consistent theory. describing it all. And that's really what's driven us to try to construct that unified theory. Munnery's, uh, Einstein tried to solve this puzzle, didn't he? Why did, why did he not succeed? Well, Einstein was really trying to do it prematurely. He didn't know enough about, uh, all the forces

that needed to be incorporated. So his efforts were doomed to failure, but he obviously was striving for what, uh, Brown Green's colleagues are still striving for. And I think the interesting question is, uh, what are the prospects of success? because first of all, as Brown Green said, the scale of these strings is far, far smaller we can directly measure. And also they involve very, very complicated geometry, not just three dimensions, but ten or eleven dimensions. And so, first of all, they involve mathematics, which for the first time is challenging mathematicians. I mean, Einstein used maths that was on the shelf already from the 19th century, so did the pioneers of quantum theory. but the mathematics needed for super string theory is still challenging mathematicians.

So we've got to learn more mathematics. It's the first time in science we needed more mathematics to make a scientific breakthrough. But the other point is... Really, the first time ever? Well, maybe not quite the first time, but if we think of the great advances in science, they've normally used maths, which to puckered mathematicians is fairly old-fashioned and standard, whereas that's certainly not the case for what they're thinking about in superstrings.

But the other issue really is how will we test it right? Because we can't directly probe these strings. We will hope that one can understand well enough the theory that you can actually calculate something about ordinary atoms, ordinary electrons, et cetera, and the ordinary forces which we can perhaps test. And just to highlight the limitations of present knowledge of the micro-world, we know there are atoms and electrons, etc.,

and we know about different forces, but we don't know why they have those particular strength. We don't know why an electron weighs 1,800 times less than a proton and things like that. And if this super string theory succeeded in explaining some numbers that we can't yet predict, then, of course, it would gain credibility. We don't actually have to observe this tiny scale. We need to be able to calculate from it something we can directly observe, so it gives a number which we can compare with observation. And then it's another thing which interests me very much a more philosophical way.

And this relates to my book Just Six Numbers, which addresses the apparent special nature of the laws in our universe. And the question there, wouldn't I like to know what Brown-Green thinks about this, is whether this ultimate theory will lead to a unique set of laws of nature in our low-energy world, or could it be that a big bang cooled down and ended up with a quite different physics, different numbers of dimensions,

different kinds of atoms in it, etc. Because if that's the case, it will mean that we can think of our universe in a different context. And in a sense, cosmology would become rather like biology in the sense that we won't be able to explain directly the physics we see because it may be some sort of historical accident

of how our particular Big Bang behaved. And so I think it's very interesting to know whether we will ever have this theory worked out enough, whether our brains can cope with the mathematics, and also what consequences will have in the everyday world. Well, I hope that string theory ultimately will give a unique prediction for how our universe is, and that prediction agrees with what we actually see in the world around us. Because as you say, there are a bunch of numbers that people have measured fastidiously over many years, some of which you've mentioned, the mass of the electron, the mass of quarks, and the strengths of the forces and so forth.

But nobody can explain the numbers that the experimenters get. And it's not just a question of idle philosophizing, because it turns out if those numbers had been even a little bit different, a few percent different, the universe, as we know, it would not exist. It would go away. Stars, for instance, rely upon nuclear processes, which themselves require delicate interrelations between these numbers, these particle masses and so forth. and if you change those numbers, the nuclear processes go away, stars don't light up, and without stars, the universe is just a very different place. So I think perhaps the deepest question that science faces is,

why is it that those numbers have just the right values to allow stars to exist and planets to form and at least on one planet life to actually exist? So we hope that string theory will come to a unique answer, but we don't know as yet. We don't know enough about the theory to know if it will do that. In passing, Martin mentioned working in more than three dimensions. science I suggested time is the fourth dimension, but you're up to nine, 10, 11 dimensions. I just cannot, I mean, I've got no purchase on that. Can you try to give us some idea of what you're talking about there?

Sure. One remarkable feature of string theory is that it only seems to make sense. Internal consistency of the theory seems to demand that the universe have at least six and probably seven more space dimensions than we're directly aware of. So, first of all, what does that mean? Well, we all live in a universe where we freely move through three dimensions all the time. left right, back, forth, up, down. Three independent directions. Include time, as you mentioned, that takes you to four. We're saying that there are six more, probably seven more space dimensions beyond the ones that we know about.

How do you think of that? Well, I think an analogy helps get the idea across. If you imagine in your mind's eye, say a big, long piece of a garden hose that you stretch out between two posts and a field, and you walk maybe a half a mile away from that garden hose, and you look back on it, Well, it's going to look like a one-dimensional line, excuse me, because you can't actually see the thickness of the garden hose from a distant vantage point. So if a little ant were living out its life on the hose, you'd say, well, it can move in the left-right dimension, but that's it, only one direction in which it can move on the surface of the hose.

But then if you take a pair of binoculars, for example, you zoom in on the garden hose, you now see that it has thickness. You now see, in fact, there's a second dimension, a dimension that's curled around the surface of the garden hose. So the little ant can not only walk in the left-right direction, it can also move counterclockwise or clockwise, a new direction that you only know about if you can zoom in and really magnify the object that you're looking at. Well, we think the universe may be very similar to that. There are three big, obvious space dimensions like the unfurled extent of the garden hose, but there may be others, perhaps seven more curled up dimensions like the circular girth of the garden hose. But we think that perhaps they're so tiny that as yet nobody has. the equipment necessary to magnify them to a scale that we can actually see. And that's how we make sense of this rather strange prediction

that there are more dimensions than meet the eye. Why do you choose seven and why are they significant? Well, when you study the mathematics of string theory, it turns out that there are equations that demand that particular number. Basically, there's roughly an equation that says, unless there's seven more dimensions, this theory falls apart. So we pick that number in order that the theory makes sense, and then we go forward and see what else it has to say about the universe.

Is this entirely speculative imaginative? I mean, what empirical evidence is being brought to bear on this at all? Is this just mathematicians having fun? Is this angels dancing on the head of a needle? I don't think so. I don't think it's angels dancing on the head of a pin because we do believe that gener relativity describes gravity because experiments have shown it.

We do believe that quantum mechanics describes the microscopic realm because experiments have shown that. We also feel that there should be one theory that puts them together in a consistent package and string theory is a theory which does that. So there is experimental support for the two underlying structures of the theory, and then we have to see what that union,

that consistent union tells us, and one strange fact is it seems to tell us that there are more dimensions. Let me just add to that. There is an experiment that's going to be carried out in the next couple years in the United States

at Stanford University and in Colorado, where experimenters are going to try to search for signatures of the extra dimensions by very, very accurate measurements of gravity on tiny sub-millimeter scales.

So it's a long-shot experiment, but it's possible that with those experiments they will get indirect evidence for the existence of these extra dimensions. And if those experiments are positive, I think it's going to be one of the most dramatic discoveries of all time. Why? Martin Rees, why do you think that'll be

most romantic discoveries of all time? Well, it'll certainly, if it works, be telling us something new about the fundamental nature of space and time and being at least a step towards unification, it will indicate on the right lines. And of course, that will increase the chance

that perhaps we will one day this century perhaps have this theory that will explain the basic forces of nature. But I think it's very important for physicists when they talk about this to emphasize that this is just one branch of physics and physics is just one science. And I think we have to be modest and realize

that for most of the rest of science, this theory is going to be entirely irrelevant. And let me give an analogy here. My favourite analogy is with a game of chess. If you imagine watching people playing chess, then eventually you could figure out what the rules were. But of course what makes chess interesting is not the rules, but the enormous complications that they allow in the play.

And what we are doing in physics is to try to understand the basic rules that govern nature. But just as in chess, simple rules, 64 squares on the board, six types of pieces, allows immense complication. So when we've got these rules playing out in our vast cosmos, then of course what they allow is all the complexity of the everyday world and the astronomical world and all the complexity. And so it is that which is the unending quest for science.

And another way to put this is that in the case of science, we can highlight three frontiers, the very big, the very small and very complicated. What we're trying to do is to unify the very big and the very small. That's what super string theory may do, but the greatest frontier of all, which most of science is concerned with, is the very complicated, and that is the unending challenge of science.

And you don't think string theory will necessarily address that? Well, I think it won't be relevant to that, because if you're a biologist or a chemist, you don't really care about what's happening inside an atom, and you care still less about what's happening on scales a billion, billion times smaller than an atom. And so it deepens our insight. It's a great philosophical importance to all of science,

but I think Brown Green would agree that to the practitioners of most sciences, it's a philosophical interest, but it doesn't affect the work they do because we can't actually do a calculation from this level for a single atom, certainly not for anything complicated. But to come back to where we started at Brian Green, the grand unified theory, the theory of everything, there's an expectation in those very phrases

that it'll be Shazam, boom, all will be solved and the Big Bang will be solved and by having a theory of everything, by uniting these two theories, we will know in a fundamental way which will permeate everything else that we know. It's no fortunate name in my opinion. Do you think that that's so?

Well, I think, as we discussed before, that string theory may well one day give us an explanation for the Big Bang, how the UNICE began and how it evolved from its state way back then, maybe 15 billion years ago, to the form we witnessed on a dark, starry night. But it's certainly the case as well that we are limited in our ability to go from the fundamental rules, as Martin Rees was saying, to understand the most complex things around us, the brain, for instance, psychology.

I don't think anyone's ever going to understand depression from the point of view of string theory. but we will understand other more simple questions such as how the universe began, how a black hole exists, what it's like to be at the center of a black hole. Those, it turns out, are far simpler questions than understanding a question like depression because we're talking about the fundamental structure of our universe, and that, I think, is a compelling kind of question to try to address. Mind you, I mean, I'm treading very, very carefully here with you two, but it is as being proved true again and again

over the last few hundred years that you don't know what the outcome of these discoveries are. I mean, Newton's laws of motion led to things that he could not have imagined and so on. Yes, absolutely. One always has to bear in mind that discoveries which seem abstract and esoteric today can sometimes have important implications

for things in the future. So could well be the case with string theory as well. Thank you very much, Brian Greene. Excellent book, The Elegant Universe. Martin Rees, excellent book, just six numbers. Thank you very much for listening. We hope you've enjoyed this Radio 4 podcast. You can find hundreds of other programmes about history, science and philosophy

at BBC.com.com.uk forward slash radio 4.