Wis- en natuurkundige Sir Roger Penrose denkt dat ons heelal weleens cyclisch zou kunnen zijn. Hoe kwam hij op dat idee?

In KIJK 12/2011 vind je een interview met de Britse wis- en natuurkundige Sir Roger Penrose (1931), over zijn zogenoemde cyclische conforme kosmologie. Kort gezegd houdt dit idee in dat zich in de verre toekomst van ons heelal de oerknal bevindt van een volgend heelal. Daarnaast correspondeert onze eigen oerknal met de verre toekomst van een vórig heelal.

Helaas konden we niet alles wat Penrose tijdens ons anderhalf uur durende gesprek vertelde kwijt in KIJK; het aantal woorden dat op vier pagina’s past, is nu eenmaal beperkt. Maar gelukkig is er internet, dat niet maalt om een alineaatje meer of minder.

Daarom hierbij, voor de natuur- en sterrenkunde-diehards, een flink fragment van het interview, in het Engels. Penrose geeft hierin antwoord op de vraag hoe hij tot zijn controversiële idee kwam.

Roger Penrose: “Well, I have to say there are two aspects to this. One is work that I had done for many years, going back to the, oh, nineteen seventees, certainly, which had to do with understanding how to talk about radiation in general relativity. When you have two stars going around each other, according to Einstein’s theory, they will emit gravitational waves. So these are the gravitational version of light. Light is an electromagnetic phenomenon, but gravity in this respect is similar to light and you have waves also; ripples in spacetime. And these are known to exist from observation, although they have not been directly detected yet – they have not been received, but they have been known from mass loss from systems. These waves carry off energy. And studying things like energy, in Einstein’s theory, is quite a difficult problem, because in any other area, energy is localized. So in an electromagnetic field, you can say how much energy is in a certain region. And there is a formula – this goes back to Maxwell, who understood about the energy carried by electromagnetic waves. Now, in gravitational theory, energy is a slippery character. You cannot localize it; you cannot say the energy is so much here, so much there, so much over here. You have to say: overall, there is so much energy, and it’s not localized anywhere. And this is a fundamental difficulty in understanding energy carried by gravitational waves.

“So I developed a certain technique, which was based originally on many calculations that other physicists had done, most particular Herman Bondi and Rainer Sachs. And they had developed a very good way of talking about the energy. But it was for me an awkward description, because it was not geometrical; it depended on doing rather complicated analytic calculations. And I like to do things geometrically; I have to see the geometrical way of what’s happening. So I developed this way of looking at it, which involves squashing down infinity to somewhere finite.

“A very good illustration of this is in M.C. Escher’s Circle Limit pictures, the most famous one being, I think, Circle Limit IV, with the angels and the devils. The whole universe of angels and devils is within one circle. And they crowd up around the edge, and you can see that’s the infinity of this universe is squashed up at the boundary. And that is a conformal map, which is the same kind of idea as I am using here, where you can squash down infinity to a finite place. And then you can do finite calculations, finite geometrical ideas, to understand things which have gone out to infinity. So that’s a good way of talking about infinity; spatial infinity or temporal infinity. So this was a technique that I had developed many years ago, in the nineteen sixties originally it was, yeah.

“So these ideas were familiar to me, that’s all I am saying. And I also knew that if you had a cosmological constant – this is the term that Einstein introduced for the wrong reasons into his equations in 1917. Why I say the wrong reasons, is because he wanted at that time to have a model of the universe which was static; it never changed overall; it all remained essentially the same. This was shortly before Edwin Hubble discovered convincingly that the universe is expanding, and so this model is not the appropriate model. So Einstein afterwards retracted and said this was a mistake, to introduce this term into his equations.

“However, it turns out Einstein’s mistake was actually correct. When I say correct, what I mean is that from about 1998, two groups of observational cosmologists, one headed by Saul Perlmutter, the other by Brian Schmidt, were looking at distant supernova stars – exploding stars – and they came to the conclusion that the universe is accelerating in its expansion. And this can be explained by Einstein’s term, the cosmological constant.

“They tended to say this in what I regard as an unfortunate way; people tended to call it dark energy. Some mysterious force, you see, is the way it was referred too, as a big mystery. Now I am puzzled by this, because as an old cosmologist, I am perfectly aware that all cosmology books, all serious cosmology books that I have ever come across mention the cosmological constant. So it’s part of cosmology. So the fact that there might be such a number in the equations has been part of standard cosmology, ever since 1917. But most people thought that number was zero. That includes me. If you’d asked me, do I think it’s zero, I should have guessed ‘yes, it’s zero’. And it’s close to zero, it’s very small. And I think the puzzle people find is why should it be so small, just at the size that we can only begin to see it now, which is a sort of coincidence in a way, yet it’s there. And so they try to say ‘well, maybe it’s something else, which we could call dark energy’. I don’t like the term because it’s not energy in any normal sense of the word. It’s something quite different, which is easily explained by Einstein’s cosmological constant. Observations at the moment, as I understand them, are completely consistent with it being a cosmological constant. It might be something else, and that could show up in observations. This has not happened, not yet in a way. So I’m very happy with it being a cosmological constant.

“And if you include a cosmological constant which is positive, then the nature of infinity, and I knew this since the nineteen sixties, is different. And that the surface which represents the boundary of spacetime in the future, is what we call spacelike. Now that’s a technical term, that’s the best I can say. I can explain a little bit more… It’s like a moment in time, but that moment is infinity.

“But the important thing for me is that it is also true that the big bang. If you stretch – now this is completely the opposite thing to do – instead of squashing infinity to make it a finite boundary, you stretch the big bang to make it a finite boundary. It’s now finite in a different sense. It’s finite in the sense that the densities are finite. The temperatures are finite, the pressure’s finite, everything is finite.

“This is basically an idea that was developed primarily by my colleague Paul Tod, and he was trying to find a nice, mathematical formulation of what I had referred to as the Weyl curvature hypothesis. Now this is a hypothesis; it’s not a theorem or an observational fact, particularly, although it is based on observation, which is a basis for the second law of thermodynamics. Now this is something which has worried me for a very long time. This very fundamental law of physics, which is known as the second law of thermodynamics, which in colloquial terms is telling us that things get more random as time goes on. But, you see, if things get more random as time goes on, this tells you that things get less random as you get back in time. So the big bang must have been a very special, non-random event. And this seems very puzzling, because it seems like a very chaotic random event, particularly since the observations of the microwave background – this is the most direct evidence we have of the big bang – what people refer to as the flash of the big bang, cooled down by the expansion – and it has this character of looking like thermal equilibrium, which means maximum entropy, which would be a contradiction, because it should be very small entropy.

“The reason it’s not a contradiction, is because what you’re looking at, in the microwave background, is matter and radiation in equilibrium. What you’re not looking at, at least what you’re not looking at in the same way, is gravity. You are actually looking at gravity too, but you’re looking at gravity because the background is very uniform for the whole sky. And that means that the universe was very uniform. And that means that the big bang was very uniform, and that means gravity had not had time to become activated, because gravity is a non-uniforming force. It tends to produce clumping; it makes stars hold together, planets, galaxies hold together through gravity. And if there were no gravity, we would have the universe dispersed all over. But the way that the entropy is low, in the initial state, is purely through gravity. And I have always thought this was a huge mystery. Because as Lee Smolin had recently described it in a review in Nature of my book, Cycles of time: in the big bang, there were two completely different temperatures. There’s a temperature of matter and electromagnetic radiation, which is very very high, and there is the temperature of gravity, which is very very low. And it’s this imbalance, between these two very different temperatures, which is what gave the universe its very low initial entropy. So everything going on of interest in the universe now, which depends upon the second law of thermodynamics, we owe that to this huge imbalance that was present in the big bang.

“Now this had always been a puzzle to me and it felt that this is one of the big things that need explaining. And the common view had been, and it had been my view also, that you need a theory of quantum gravity to explain the structure of the big bang. But this had always been confusing to me, because you have two theories, which are basically symmetrical in time: the quantum evolution procedures, and the gravitational theory. And yet, so the theory goes, we should see a big bang which is stupendously asymmetrical in time. That is to say, you have this enormous imbalance between gravity and the rest of physics, which is what gave us the second law of thermodynamics. If the universe were to collapse and have what we call a big crunch, this would not be the case. Everything would be thermalized, gravity also, and it wouldn’t look the slightest bit like the time reverse of the big bang. So we have a huge mystery. And that mystery – I had said, well, I invented the Weyl curvature hypothesis as pushing the mystery in a hypothesis; it’s still a mystery.

“Now my colleague Paul Tod had a nice way of phrasing the Weyl curvature hypothesis. And his way of phrasing it is just what I was saying: you stretch the big bang, and the hypothesis is now that it is smooth. And that smooth initial state is something that you could imagine extending prior to it. Now here is where conformal geometry comes in. People are used to think of geometry in terms of distances and times. Now, and Einstein, for his general theory of relativity, needed the concept of what’s called the metric, you see; he had this thing called the metric tensor, which tells you the rate at which time progresses, and hence, therefore, also the scale of space. So the scale of space and time are fixed by this metric.

“Now it happens to be the case that a great deal of physics is not interested in the full metric. Now let me explain: the metric that comes fundamental with Einstein’s theory requires ten numbers at each points. These are called the components of a metric tensor. And you need to know those ten numbers to know what the metric is. Now if you’re only interested in the ratios between those ten numbers, which is nine independent numbers, so you can scale the ten up or down all together, that’s now only nine numbers needed for that information. That’s what’s called the conformal geometry. Now the conformal geometry – another way of saying the conformal geometry is what’s called the light cone structure, or the null cone structure. That means at any point, you know how light would behave; you know what a flash of light would do. And knowing that, you don’t know the full metric, you only know the nine ratios of the ten numbers. But those nine numbers are quite sufficient; we’re doing an awful lot of physics. And Maxwell’s theory of electromagnetism, and this has been one of the great triumphs of theoretical physics in the nineteenth century, showed how light comes about by an interplay between electric and magnetic fields, and also how electric charges and electric currents are the source of this electricity and magnetism. Now those two concepts satisfy equations, Maxwell’s equations, which are what I called conformally invariant. So they don’t need to know the scale. If you only specify these nine ratios, Maxwell tells you what to do.

“So you asked me, what was the big idea, and now I can say the big idea. So far I have been talking about background. The big idea is always something within a context. And the context was, I was worrying about the boring universe we shall inhabit – or we won’t be. I was thinking about this exciting world we live in, now, and what is the future of this? But according to standard cosmology, the universe will expand, and expand, and expand, and get colder, and colder, and colder, and the most exciting things left, in the remote future, will be the disappearance of black holes, by Stephen Hawking’s process of black hole evaporation. Black holes, he says – and I agree with him – are not exactly cold, they have a very tiny temperature.

“Okay, the hottest black holes we have any reason to believe in, in our universe, are so cold that the temperature of these objects has to be compared with the lowest temperature ever produced on Earth, artificially. So this is a very cold temperature. Bigger black holes are even colder. As the universe expands and expands and expands, the ambient temperature, which is this cosmic microwave background, gets colder and colder and colder, and eventually it becomes colder than even the coldest black holes. Then the black holes are hotter than the background, and they radiate away energy, as they radiate energy away they radiate mass away, E=mc^2, and so they shrink, because smaller black holes are less massive. So they lose mass, they lose this substance, and eventually they disappear with a ‘pop’. I call it a pop and not a bang because, okay, it’s like an artillery shell or something like that, which on the cosmic scale is ridiculously small. And so this is the most exciting thing left in the universe. Yeah, I can’t imagine anything much more boring; waiting for a black hole to evaporate. After that, it’s the very boring universe, when there are no black holes left.

“And I just thought, and I admit that this is an emotional argument, that this is a pretty ignominious fate for our wonderful universe. But then I thought: who is going to be bored by this boring universe? Not us. Only things like photons, with no mass. And it’s very hard to bore a photon. It’s hard to bore a photon because on the one hand, it probably has no experiences, but on the other hand, it does not experience the passage of time. So anything with no mass, like a photon, it can reach this final boundary. You see, it had been my experience with these corformal maps, you think of making infinity into a finite boundary like in the Escher picture. And then you say, what is outside that? If you’re a massless thing, you just go right through. This boundary is of no interest to you; you cross it. And so, do you just disappear, or is there something on the other side?

“So that’s question number one. Question number two is the other end of the scale, and this is where Paul Tod comes in. He says, well, if we want to represent the big bang which encompasses this paradoxical imbalance between gravity and everything else, we say ‘okay, you can stretch the big bang out, and you can extend it to something prior to the big bang’. Now the physics underlying this would be, well, the big bang is very hot. The closer you get to the big bang, the hotter it gets. It gets so hot that rest mass, the mass of particles, becomes irrelevant. This is already beginning to be the case with the LHC. When people say they are trying to find the Higgs particle, they are basically trying to ask the question: where does mass enter the universe? At what temperature, at what scale, do we start to see mass? So the idea is that hotter than that, earlier than that in the big bang, there is in effect no mass.

“If there is no mass, again, the particles are not really interested in this boundary; they maybe came from somewhere prior to the boundary. So you see, I’m laying the stage for the crazy idea, which is that what is beyond the remote future, is another big bang of another aeon, as I call it. What was prior to our big bang, was the infinity of a previous aeon.

“So if you like, that was the idea which came to me… nearly six years ago, in August 2005. And at the time, I suppose my initial reaction was, oh, this fits nicely, but crazy, you see. [lacht] I used to give lectures, calling it a crazy idea. But I was kind of, I think, being defensive. I was trying to think, ‘well, other people will say this man is crazy; he is talking about crazy scheming’, so I would say it was crazy first, before they’d say it. [lacht] But all the time, I had a suspicion it fits so nicely, maybe it’s true. And we need a crazy idea. So I think my experiences since that time have been that the idea does seem to work quite well, and even in the most recent analyses of observations there is some evidence for this scheme.”

Een Nederlandstalige, compactere en toegankelijkere versie van dit interview vind je in KIJK 12/2011. Dit nummer ligt in de winkel van 21 oktober tot en met 17 november.

Beeld: Biswarup Ganguly/CC BY 3.0