IN THE MATRIX (p2)

(MARTIN REES:) This is a really good time to be a cosmologist, because in the last few years some of the questions we've been addressing for decades have come into focus. For instance, we can now say what the main ingredients of the universe are: it's made of 4% atoms, about 25% dark matter, and 71% mysterious dark energy latent in empty space. That's settled a question that we've wondered about, certainly the entire 35 years I've been doing cosmology.

We also know the shape of space. The universe is 'flat'—in the technical sense that the angles of even very large triangles add up to 180 degrees. This is an important result that we couldn't have stated with confidence two years ago. So a certain phase in cosmology is now over.

But as in all of science, when you make an advance, you bring a new set of questions into focus. And there are really two quite separate sets of questions that we are now focusing on. One set of questions addresses the more 'environmental' side of the subject—we're trying to understand how, from an initial Big Bang nearly 14 billion years ago, the universe has transformed itself into the immensely complex cosmos we see around us, of stars and galaxies, etc.; how around some of those stars and planets arose; and how on at least one planet, around at least one star, a biological process got going, and led to atoms assembling into creatures like ourselves, able to wonder about it all. That's an unending quest—to understand how the simplicity led to complexity. To answer it requires ever more computer modeling, and data in all wavebands from ever more sensitive telescopes.

Another set of questions that come into focus are the following:

•   Why is the universe expanding the way it is?
•   Why does it have the rather arbitrary mix of ingredients?
•   Why is it governed by the particular set of laws which seem to prevail in it, and which physicists study?

These are issues where we can now offer a rather surprising new perspective. The traditional idea has been that the laws of nature are somehow unique; they're given, and are 'there' in a platonic sense independent of the universe which somehow originates and follows those laws.

I've been puzzled for a long time about why the laws of nature are set up in such a way that they allow complexity. That's an enigma because we can easily imagine laws of nature which weren't all that different from the ones we observe, but which would have led to a rather boring universe—laws which led to a universe containing dark matter and no atoms; laws where you perhaps had hydrogen atoms but nothing more complicated, and therefore no chemistry; laws where there was no gravity, or a universe where gravity was so strong that it crushed everything; or the lifetime was so short that there was no time for evolution.

It always seemed to me a mystery why the universe was, as it were, 'biophilic'—why it had laws that allowed this amount of complexity. To give an analogy from mathematics, think of the Mandelbrot Set; there's a fairly simple formula, a simple recipe that you can write down, which describes this amazingly complicated pattern, with layer upon layer of structure. Now you could also write down other rather similar-looking recipes, similar algorithms, which describe a rather boring pattern. What has always seemed to me a mystery is why the recipe, or code, that determined our universe had these rich consequences, just as the algorithms of the Mandelbrot set rather than describing something rather boring, in which nothing as complicated as us could exist.

For about 20 years I've suspected that the answer to this question is that perhaps our universe isn't unique. Perhaps, even, the laws are not unique. Perhaps there were many Big Bangs which expanded in different ways, governed by different laws, and we are just in the one that has the right conditions. This thought in some respect parallels the way our concept of planets and planetary systems has changed.

People used to wonder: why is the earth in this rather special orbit around this rather special star, which allows water to exist or allows life to evolve? It looks somehow fine-tuned. We now perceive nothing remarkable in this, because we know that there are millions of stars with retinues of planets around them: among that huge number there are bound to be some that have the conditions right for life. We just happen to live on one of that small subset. So there's no mystery about the fine-tuned nature of the earth's orbit; it's just that life evolved on one of millions of planets where things were right.

It now seems an attractive idea that our Big Bang is just one of many: just as our earth is a planet that happens to have the right conditions for life, among the many many planets that exist, so our universe, and our Big Bang, is the one out of many which happens to allow life to emerge, to allow complexity. This was originally just a conjecture, motivated by a wish to explain the apparent fine-tuning in our universe—and incidentally a way to undercut the so-called theological design argument, which said that there was something special about these laws.

But what's happened in the last few years, and particularly  sin the last year, is that the basis for this so-called multiverse idea has strengthened, and, moreover, the scale which we envisage for the multiverse has got even vaster than we had in mind a few years ago. There's a firmer basis for the 'multiverse' concept because recent work on the best theory we have for the fundamental laws of nature, namely superstring theory, suggests that there should indeed be many possible forms for a universe, and many possible laws of nature.

At first it was thought that there might be just one unique solution to the equations, just one possible three-dimensional universe with one possible 'vacuum state' and one set of laws. But it seems now, according to the experts, that there could be a huge number. In fact Lenny Susskind claims that there could be more possible types of universe than there are atoms in our universe—a quite colossal variety. The system of universes could be even more intricate and complex than the biosphere of our planet. This really is a mind-blowing concept, especially when we bear in mind that each of those universes could themselves be infinite.

At first sight you might get worried about an infinity of things in themselves infinite, but to deal with this you have to draw on a body of mathematics called transfinite number theory, that goes back to Cantor in the 19th century. Just as many kinds of pure mathematics have already been taken over by physicists, this rather arcane subject of transfinite numbers is now becoming relevant, because we've got to think of infinities of infinity. Indeed, there's perhaps even a higher hierarchy of infinities: in addition to our universe being infinite, and there being an infinite number of possible laws of nature, we may want to incorporate the so-called many worlds theory of quantum mechanics.

Each 'classical' universe is then replaced by an infinite number of super-imposed universes, so that when there's a quantum choice to be made the path forks into extra universes. This immensely complicated construct is the consequence of ideas that are still speculative but are firming up. One of the most exciting frontiers of 21st century physics, is to utilize the new mathematics and the new cosmology to come to terms with all this.