Three Roads to Quantum Gravity (7 page)

We are used to the idea that a physical theory can describe an infinitude of different worlds. This is because there is a lot of freedom in their application. Newton’s physics gives us the laws by which particles move and interact with one another, but it does not otherwise specify the configurations of the particles. Given any arrangement of the particles that make up the universe, and any choices for their initial motions, Newton’s laws can be used to predict the future. They thus apply to any possible universe made up of particles that move according to their laws. Newton’s theory describes an infinite number of different worlds, each connected with a different solution to the theory, which is arrived at by starting with the particles in different positions. However, each solution to Newton’s theory describes a single universe. This is very
different from what seems to be coming out of the equations of the conventional approach to quantum cosmology. There, each solution seems to have within it descriptions of an infinite number of universes. These universes differ, not only in the answers that the theory gives to questions, but by the questions that are asked.

Everett’s relative-state form of the theory must therefore be supplemented by a theory of why what we observe corresponds to the answers to certain questions, and not to an infinite number of other questions. Several people have attempted to deal with this, and some progress has been made using an idea called decoherence. A set of questions is called decoherent if there is no chance that a definite answer to one is a superposition of definite answers to others. This idea has been developed by several people into an approach to quantum cosmology called the consistent histories formulation. This approach lets you specify a series of questions about the history of the universe. Assuming only that the questions are consistent with one another, in the sense that the answer to one will not preclude our asking another, this approach tells us how to compute the probabilities of the different possible answers. This is progress, but it does not go far enough. The world we experience is decoherent but, as has been convincingly shown by two young English physicists, Fay Dowker and Adrian Kent, so are an infinite number of other possible worlds.

One of the most dramatic moments I’ve experienced during my career in science was the presentation of this work at a conference on quantum gravity in Durham, England, in the summer of 1995. When Fay Dowker began her presentation on the consistent histories formulation, that approach was generally regarded as the best hope for resolving the problems of quantum cosmology. She was a postdoc under James Hartle, who had pioneered the development of the consistent histories approach to quantum cosmology, and there was little indication in her introduction of what was coming. In a masterful presentation she built up the theory, elucidating along the way some of its most puzzling aspects. The theory seemed in better shape than ever. Then she proceeded to
demonstrate two theorems that showed that the interpretation did not say what we thought it did. While the ‘classical’ world we observe, in which particles have definite positions, may be one of the consistent worlds described by a solution to the theory, Dowker and Kent’s results showed that there had to be an infinite number of other worlds too. Moreover, there were an infinite number of consistent worlds that have been classical up to this point but will not be anything like our world in five minutes’ time. Even more disturbing, there were worlds that were classical now that were arbitrarily mixed up superpositions of classical at any point in the past. Dowker concluded that, if the consistent-histories interpretation is correct, we have no right to deduce from the existence of fossils now that dinosaurs roamed the planet a hundred million years ago.

I cannot speak for everyone who was in that room, but the people sitting near me were as shocked as I was. In conversations we had later that summer, Jim Hartle insisted that the work he and Murray Gell-Mann had done on the consistent histories approach was not contradicted by anything Fay Dowker had said. They were fully aware that their proposal imposed on reality a radical context dependence: one cannot talk meaningfully about the existence of any object or the truth of any statement without first completely specifying the questions that are to be asked. It is almost as if the questions bring reality into being. If one does not first ask for a history of the world that includes the question of whether dinosaurs roamed the Earth a hundred million years ago, one may not get a description in which the notion of dinosaurs - or any other big ‘classical objects’ - has any meaning.

I checked, and Hartle was right. What he and Gell-Mann had said was still valid. An interesting thing seems to have happened, which in retrospect is not all that unusual: many of us working on this problem had misunderstood Gell-Mann and Hartle to mean something much less radical, and much more comfortable to our classical, old-fashioned intuitions, than what they had actually proposed. There is, according to them, one history of the world, and it is expressed in quantum
language. But this one world contains many different, equally consistent histories, each of which can be brought into being by the right set of questions. Each history is incompatible with the others, in the sense that they cannot be experienced together by observers like ourselves. But each is, according to the formalism, equally real.

As you might imagine, there was a huge, if mostly friendly, disagreement over what to make of this. Some of us follow Fay Dowker and Adrian Kent in their conviction that this infinite expansion of the notion of reality is unacceptable. Either quantum mechanics is wrong when applied to the whole universe, or it is incomplete in that it must be supplemented by a theory of which set of questions corresponds to reality. Others follow James Hartle and Murray Gell-Mann in embracing the extreme context dependence that comes with their formulation. As Chris Isham says, the problem lies with the meaning of the word ‘is’.

If this were not trouble enough, there are other difficulties with this conventional formulation of quantum cosmology. It turns out that one is not free to ask any set of questions: instead, these are constrained by having to be solutions to certain equations. And, although we had solved the equations that determine the quantum states of the universe, it proved much more difficult to determine the questions that can be asked of the theory. It seems unlikely that this can ever be done - at least in any real theory, as opposed to the toy models that describe little yo-yo-like versions of the universe. Perhaps I should not comment on the likelihood of finding the right set of questions, given that our solving the equations for the states was itself a total accident. Still, we have tried, many smarter people have tried, and we have all come to the conclusion this is not a stone that can be moved. So conventional quantum cosmology seems to be a theory in which we can formulate the answers, but not the questions.

Of course, from the perspective of the last chapter, this is not surprising. We saw there that to formulate a theory of cosmology we must acknowledge that different observers see partly different, partial views of the universe. From this
starting point it makes no sense to try to treat the whole universe as it if were a quantum system in a laboratory of the kind that ordinary quantum theory applies to. Could there be a different kind of quantum theory, one in which the quantum states refer explicitly to the domain seen by some observer? Such a theory would be different from conventional quantum theory. It would in a sense ‘relativize’ that theory, in the sense that it would make the quantum theory depend more explicitly on the location of the observer inside the universe. It would describe a large, perhaps infinite set of quantum worlds, each of which corresponds to the part of the world that could be seen by a particular observer, at a particular place and time in the history of the universe.

In the past few years there have been several proposals for just such a new kind of quantum cosmology. One of them grew out of the consistent-histories approach. It is a kind of reformulation of it, by Chris Isham and his collaborator Jeremy Butterfield, in which they make context dependence the central feature of the mathematical formulation of the theory. They found that they can do this using topos theory, which allows one to describe many interrelated quantum mechanical descriptions, differing according to choice of context, in one mathematical formalism. Their work is beautiful, but difficult in the way a philosopher like Hegel or Heidegger is difficult. It is not easy to find the right language to use to talk about the world if one really believes that the notion of reality depends on the context of the person doing to the talking.

For many of us in quantum gravity, Chris Isham is a kind of theorists’ theorist. Most theoretical physicists think in terms of examples, and then seek to generalize what they have learned as widely as possible. Chris Isham seems to be one of the few people who can work productively in the other direction. Several times he has introduced important ideas in a very general form, leaving it to others to apply the lessons to particular examples. On one occasion this led to loop quantum gravity, when Carlo Rovelli saw in a very general idea of his a strategy that could pay off in very concrete terms. Something like this is happening now. People have been
thinking about context dependence in quantum cosmology for about ten years. We have learned from Chris Isham what kind of mathematics we need to do this.

Before Isham and his collaborators, Louis Crane, Carlo Rovelli and I developed different versions of an idea we called relational quantum theory. Going back to our earlier feline example, the basic idea was that all the players have a context, which consists of the part of the world they describe. Rather than asking which quantum description is right - that of the mouse, the cat, me, my friend - we argued that one has to accept them all. There are many quantum theories, corresponding to the many different possible observers. They are all interrelated, because when two observers are able to ask the same question they must get the same answer. The mathematics of topos theory, as developed by Chris Isham and collaborators, has told us how to do this for any possible case in which it may arise.

A third context-dependent theory was formulated by Fotini Markopoulou-Kalamara, by extending her proposal for cosmological logic to quantum theory. The result is that a context turns out to be the past of an observer, at a given moment. This is a beautiful unification of quantum theory and relativity in which the geometry of light rays, that determines how information may travel, itself determines the possible contexts.

In all these theories there are many quantum descriptions of the same universe. Each of them depends on a way of splitting the universe into two parts such that one part contains the observer and the other part contains what the observer wishes to describe. Each such division gives a quantum description of part of the universe; each describes what one particular observer will see. All these descriptions are different, but they have to be consistent with one another. This resolves the paradox of superpositions by making it a consequence of one’s point of view. The quantum description is always the description of some part of the universe by an observer who remains outside it. Any such quantum system can be in a superposition of states. If you observe a system that includes me, you may see me in a superposition of states. But I do not
describe myself in such terms, because in this kind of theory no observer ever describes themself.

Many of us believe that this is a definite step in the right direction. Rather than trying to make sense of metaphysical statements about their being many universes - many realities - within one solution to the theory of quantum cosmology, we are constructing a pluralistic version of quantum cosmology in which there is one universe. That universe has, however, many different mathematical descriptions, each corresponding to what a different observer can see when they look around them. Each is incomplete, because no observer can see the whole universe. Each observer, for example, excludes themselves from the world they describe. But when two observers ask the same question, they must agree. And if I look around tomorrow it cannot happen that the past changed. If I see dinosaurs roaming today on a planet a hundred million light years away, they will still be roaming there when I receive signals from the planet next year.

Like all advocates of new ideas, we support our opinions with slogans as well as with results. Our slogans are ‘In the future we shall know more’ and ‘One universe, seen by many observers, rather than many universes, seen by one mythical observer outside the universe’.

I
magine you are trying to explain to someone why you are so enamoured of your new girlfriend or boyfriend, and someone quite sensibly asks you to describe them. Why do our efforts on such occasions seem so inadequate? Your intuition tells you that there is something essential about this person, but it is very hard to put it into words. You describe what they do for a living, what they like to do for fun, what they look like, how they act, but somehow this does not seem to convey what they are really like.

Or imagine that you have fallen into one of those interminable discussions about culture and national characteristics. It seems so obvious that the English are different from the Greeks, who are nothing at all like the Italians, except that they are both different from the English in the same way. And how is it that the Chinese seem in certain ways a bit American in their spirit, when their cultural history is so different and so much older? Again, it seems that there is something real here, but most of our attempts to capture it in words seem to fall short of what we are trying to express.

There is a simple solution to these quandaries: tell a story. If we narrate the story of our new friend’s life, where and how they grew up, who their parents are and how they raised them, where they studied, what happened in their past relationships, we communicate more of what is important about them than if we attempt to describe how they are now. The same goes for cultures. It is only when we know something
about their histories, both recent and ancient, that we begin to gain any insight into why being human is expressed a bit differently in different parts of the world. This may be obvious, but why should it be so? What is it about a person or a culture that makes it so hard to describe without telling a story? The answer is that we are not dealing with a thing, like a rock or a can opener. These are objects which remain more or less the same from decade to decade. They can be described, for most purposes, as static objects, each with some collection of unchanging properties. But when we are dealing with a person or a culture we are dealing with a process that cannot be comprehended as a static object, independently of its history. How it is now is incomprehensible without knowing how it came to be.