Three Roads to Quantum Gravity (28 page)

Looking back, it is clear that the assumption that a unified theory would be unique was no more than that - an assumption. There is no mathematical or philosophical principle which guarantees there to be only one mathematically consistent theory of nature. In fact, we now know that there can be no such theory. For example, suppose that the world had one or two spatial dimensions, rather than three. For these cases we have constructed lots of consistent quantum theories, including some which have gravity. These were done as warm-up exercises for various research
programmes. We keep them around as experimental laboratories in which we can test new ideas in a context where we know we can calculate anything we like. It is always possible that there is only one possible consistent theory to describe worlds that have more than two spatial dimensions. But there is no known reason why this should be true. In the absence of any evidence to the contrary, the fact that there are many consistent theories that describe one- and two-dimensional universes should lead us to doubt the assumption that mathematical consistency in itself allows only one theory of nature.

Of course, there is a way out, which is the possibility that string theory is not the final theory. Besides the fact that it comes in many versions, there are good reasons to believe this: string theory is background dependent and it is understood only in terms of a certain approximation scheme. A fundamental theory needs to be background independent and capable of being formulated exactly. So most people who work with string theory now believe the M theory conjecture I described in Chapter 11: that there is a single theory, which can be written down exactly and in a way that is independent of any given spacetime, that unifies all the different string theories.

There is some evidence to support this M theory conjecture. Many physicists, myself included, are now trying to invent the theory. There seem to be three possibilities:

If possibility 1 is true, then all we can do is take the story of string theory as a cautionary tale. So let us put this one aside and look at the others. If possibility 2 is true, then we are left with a puzzle: what or who chose which consistent theory applies to our world? Among the list of different possible consistent theories, how was one chosen to apply to our universe?

There seems to be only one possible answer to this question. Something external to the universe made the choice. If that’s the way things turn out, then this is the exact point at which science will become religion. Or, to put it better, it will then be rational to use science as an argument for religion. One already hears a lot about this in theological circles, as well as from certain scientists, in the form of arguments based on what we might call the anthropic observation. It seems that the universe we live in is very special. For a universe to exist for billions of years and contain the ingredients for life, certain special conditions must be satisfied: the masses of the elementary particles and the strengths of the fundamental forces must be tuned to values very close to the ones actually we observe. If these parameters are outside certain narrow limits, the universe will be inhospitable to life. This raises a legitimate scientific question: given that there seem to be more than one possible consistent set of laws, why is it that the laws of nature are such that the parameters fall within the narrow ranges needed for life? We may call this the anthropic question.

If there are different possible consistent laws of nature, but no framework which unifies them, then there are only two possible answers to the anthropic question. The first is that we are very lucky indeed. The second is that whatever entity specified the laws did so in order that there would be life. In this case we have an argument for religion. This is of course a version of an argument which is well known to theologians - the God of the Gaps argument. If science raises a question like the anthropic question that cannot be answered in terms of processes that obey the laws of nature, it becomes rational to invoke an outside agency such as God. The scientific version of this argument is called the strong anthropic principle.

Notice that this argument is valid only if there is no way to explain how the laws of nature might have been chosen except by invoking the action of some entity outside our universe. You may recall the principle with which I started this book: that there is nothing outside the universe. As long as there is a way of answering all our questions without violating this principle, we are doing science and we have no need of any other mode of explanation. So the argument for the strong anthropic principle has logical force only if there is no other possibility.

But there is another possibility, possibility 3. This is like possibility 2, but with an important difference. If the different string theories describe different phases of a single theory, then it is possible that under the right circumstances there could be a transition from one phase to another. Just as ice melts to water, the universe could ‘melt’ from one phase, in which it is described by one string theory, to another phase, in which it is described by another. We are then still left with the question of why one phase rather than another describes our universe, but this is not so hard to resolve because in this picture the universe is allowed to have changed phase as it evolved in time. There is also the possibility that different regions of the universe exist in different phases.

Given these possibilities, there are at least two alternatives to the God of the Gaps argument. The first is that there is some process that creates many universes. (Do not worry for the moment about what that process is, for cosmologists have found several attractive ways to make a universe which continually spawns new universes.) The big bang is then not the origin of all that exists, but only a kind of phase transition by which a new region of space and time was created, in a phase different than the one from which it came, and then cooled and expanded. In such a scenario there could be many big bangs, leading to many universes. The astrophysicist Martin Rees has a nice name for this - he calls the whole collection the ‘multiverse’. It is possible that the process creates universes in random phases. Each would then be governed by a different string theory. These universes will have different dimensions and geometries, and they will also
have different sets of elementary particles which interact according to different sets of laws. If there are adjustable parameters, it is possible that they are set at random each time a new universe is created.

So there is a simple answer to the anthropic question. Among all the possible universes, a minority will have the property that their laws are hospitable to life. Since we are alive, we naturally find ourselves in one of them. And since there are a great many universes, we need not worry that the chance of any one of them being hospitable to life is small, because the chance of at least one of them being hospitable to life may not be small. There will then be nothing to explain. Martin Rees likes to put this in the following way: if one finds a bag by the side of the road containing a suit that fits one perfectly, that is something to wonder about. But if one goes into a clothing store and is able to find a suit that fits, there is no mystery because the store carries lots of suits in many different sizes. We may call this the God of The Gap. It is also sometimes called the weak anthropic principle.

The only problem with this kind of explanation is that it is difficult to see how it could be refuted. As long as your theory yields a very large number of universes, you only need there to be at least one like ours. The theory makes no other predictions apart from the existence of at least one universe like ours. But we already know that, so there is no way to refute this theory. This might seem good, but actually it is not because a theory that cannot be refuted cannot really be part of science. It can’t carry very much explanatory weight, because whatever features our universe has, as long as it can be described by one of the large number of string theories, our theory will not be refuted. Therefore it can make no new predictions about our universe.

Is it possible to have a theory which gives a scientific answer to the anthropic question? Such a theory may be framed around the possibility that the universe can make a physical transition from one phase to another. If we could look back into the history of the universe to before the big bang, it may be that we would see one or a whole succession of different phases in which the universe had different
dimensions and appeared to satisfy different laws. The big bang would then be just be the most recent of a series of transitions the universe has passed through. And even though each phase may be governed by a different string theory, the whole history of the universe would be governed by a single law - M theory. We then need an explanation in physical terms for why the universe ‘chose’ to exist in a phase such as the one in which we find ourselves, which exists for billions of years and is hospitable for life. There are several different possible explanations of this kind, which are described in detail in another book of mine, The Life of the Cosmos, so I shall be brief here.

One idea is that new universes could form inside black holes. In this case our universe would have a large number of progeny, as it contains at least 10
¹⁸
black holes. One may also conjecture that the changes in the laws from old universes to new are small, so that the laws in each new universe formed from our own are close to those that hold in our universe. This also means that the laws in the universe from which ours was formed were not very different from those of our own. Given these two assumptions, a mechanism which is formally analogous to natural selection operates, because after many generations those universes that give rise to many black holes will dominate the population of universes. The theory then predicts that a randomly chosen universe will have the property that it will make more black holes than will universes with slightly different values of the parameters. We can then ask whether this prediction is satisfied by our universe. To cut a long story short, up to the present time it seems that it is. The reason is that carbon chemistry is not only good for life, it plays an important role in the processes that make the massive stars that end up as black holes. However, there are several possible observations which could disprove the theory. Thus, unlike the God of the Gaps and the God of The Gap theories, this theory is very vulnerable to being disproved. Of course, this means that it is likely to be disproved.

The important thing about this theory is that it shows that there are alternatives to both the strong and the weak
anthropic principle. And if that is so, then those principles have no logical force. Beyond this, the theory of cosmological natural selection (as it is sometimes called) shows us that physics can learn an important lesson from biology about possible modes of scientific explanation. If we want to stick to our principle that there is nothing outside the universe, then we must reject any mode of explanation in which order is imposed on the universe by an outside agency. Everything about the universe must be explicable only in terms of how the laws of physics have acted in it over the whole span of its history.

Biologists have been facing up to this problem for more than a century and a half, and they have understood the power of different kinds of mechanism by which a system may organize itself. These include natural selection, but that is not the only possibility: other mechanisms of self-organization have been discovered more recently. These include self-organized critical phenomena, invented by Per Bak and collaborators and studied by many people since. Other mechanisms of self-organization have been studied by theoretical biologists such as Stuart Kauffman and Harold Morowitz. So there is no shortage of mechanisms for self-organization that we could consider in this context. The lesson is that if cosmology is to emerge as a true science, it must suppress its instinct to explain things in terms of outside agencies. It must seek to understand the universe on its own terms, as a system that has formed itself over time, just as the Earth’s biosphere has formed itself over billions of years, starting from a soup of chemical reactions.

It may seem fantastic to think of the universe as analogous to a biological or ecological system, but these are the best examples we have of the power of the processes of self-organization to form a world of tremendous beauty and complexity. If this view is to be taken seriously, we should ask whether there is any evidence for it. Are there any aspects of the universe and the laws that govern it that require explanation in terms of mechanisms of self-organization? We have already discussed one piece of evidence for this, which is the anthropic observation: the apparently improbable
values of the masses of the elementary particles and the strengths of the fundamental forces. One can estimate the probability that the constants in our standard theories of the elementary particles and cosmology would, were they chosen randomly, lead to a world with carbon chemistry. That probability is less than one part in 10
²²⁰
. But without carbon chemistry the universe would be much less likely to form large numbers of stars massive enough to become black holes, and life would be very unlikely to exist. This is evidence for some mechanism of self-organization, because what we mean by self-organization is a system that evolves from a more probable to a less probable configuration. So the best argument we can give that such a mechanism has operated in the past must have two parts: first, that the system be structured in some way that is enormously improbable; and second, that nothing acting from the outside could have imposed that organization on the system. In the case of our universe we are taking this second part as a principle. We then satisfy both parts of the argument, and are justified in seeking mechanisms of self-organization to explain why the constants in the laws of nature have been chosen so improbably.