Three Roads to Quantum Gravity

by Lee Smolin

  Just what is it about a story that tells us so much? What extra information are we conveying when we tell a story? When we tell a story about someone we narrate a series of episodes in their life. These tell us something about that person because we believe, from having heard and understood many such stories, that what happens to a person as they grow up has an effect on who they are. We also believe that people’s characters are best revealed in how they react to situations, both propitious and adverse, and in what they have sought to do or become.

  However, it is not the events themselves that carry the information in a narration. A mere list of events is very boring and is not a story. This is perhaps what Andy Warhol was trying to convey in his movies of haircuts or of a day in the life of the Empire State Building. What makes a story a story is the connections between the events. These may be made explicit, but they often do not need to be, because we fill them in almost unconsciously. We can do that because we all believe that events in the past are to some extent the causes of events in the future. We can debate to what extent a person is shaped by what happens to them, but we do not need to be devout determinists to have a practical and almost instinctive understanding of the importance of causality. It is this understanding of causality that makes stories so useful. Who did what to whom, and when, and why, is interesting because of what we know about the consequences of actions and events.

  Imagine what life would be like without causality. Suppose that the history of the world were no more than random sets of events with no causal connections at all between them. Things would just happen; nothing would remain in place. Furniture, houses, everything would just come into being and disappear. Can you imagine what that would really be like? I can’t - it is far too different from the world we live in. It is causality that gives our world its structure, that explains why this morning our chairs and tables are in the same places we left them last night. And it is because of the overwhelming importance of causal relations in shaping our world that stories are much more informative than descriptions.

  So it seems there are two kinds of thing in the world. There are objects like rocks and can openers that simply are, that may be explained completely by a list of their properties. And then there are things that can only be comprehended as processes, that can only be explained by telling stories. For things of this second kind a simple description never suffices. A story is the only adequate description of them because entities like people and cultures are not really things, they are processes unfolding in time.

  Here is an idea for an art piece. Take a film which everyone has seen and loved, and extract from it a series of stills, one from every ten seconds of the film. Mount these in a large gallery, arranged sequentially. Invite people to view the film one still at a time. Would this be enjoyable? No, people might laugh a bit at the beginning, but most would quickly become bored. Of the few who looked at the whole film, many would be film-makers and critics who would be able to pick up some tricks about how the film was made. For most of the rest of us a film presented one still at a time would be quite uninteresting, even if it took no longer to view the whole sequence than to watch the film. Of course, when we watch a film we are really looking at a sequence of still images, presented to us at such a rate that we see movement. This is sometimes described by saying that the sequence of still images creates the illusion of motion, but that is not quite right. It is the still images themselves that are the illusion. The world is never still - it is always in motion. The illusion that photography creates is of a frozen moment of time. It corresponds to nothing in reality, nor is it itself real, for any photograph is also a process. In a few years it will fade as a result of chemical processes which are always going on between the molecules that make up the apparently still image. So what happens in a movie is that the real world of motion and change is recreated from a sequence of illusions, not the reverse.

  We humans seem to be fascinated by our ability to hold back change for long periods of time. This may be why painting and sculpture are so fascinating and so valuable, for they offer the illusion of time stopped. But time cannot be stopped. A marble sculpture may look the same from day to day, but it is not: each day the surface becomes a little different as the marble interacts with the air. As the Florentines have learned only too well from the damage wrought to their heritage by pollution, marble is not an inert thing, it is a process. All the skill of the artist cannot turn a process into a thing, for there are no things, only processes that appear to change slowly on our human timescales. Even objects that seem not to change, like rocks and can openers, have stories. It is just that the timescale over which they change significantly is longer than for most other things. Geologists and cultural historians are very interested in narrating the stories of rocks and can openers.

  So there are not really two categories of things in the world: objects and processes. There are only relatively fast processes and relatively slow processes. And whether it is a short story or a long story, the only kind of explanation of a process that is truly adequate is a story.

  The illusion that the world consists of objects is behind many of the constructs of classical science. Supposing one wants to describe a particular elementary particle, say a proton. In the Newtonian mode of description one would describe what it is at a particular moment of time: where it is located in space, what its mass and electric charge are, and so forth. This is called describing the ‘state’ of the particle. Time is nowhere in this description; it is, indeed, an optional part of the Newtonian world. Once one has adequately described how something is, one then ‘turns on’ time and describes how it changes. To test a theory, one makes a series of measurements. Each measurement is supposed to reveal the state of the particle, frozen at some moment of time. A series of measurements is like a series of movie stills - they are all frozen moments.

  The idea of a state in Newtonian physics shares with classical sculpture and painting the illusion of the frozen moment. This gives rise to the illusion that the world is composed of objects. If this were really the way the world is, then the primary description of something would be how it is, and change in it would be secondary. Change would be nothing but alterations in how something is. But relativity and quantum theory each tell us that this is not how the world is. They tell us - no, better, they scream at us - that our world is a history of processes. Motion and change are primary. Nothing is, except in a very approximate and temporary sense. How something is, or what its state is, is an illusion. It may be a useful illusion for some purposes, but if we want to think fundamentally we must not lose sight of the essential fact that ‘is’ is an illusion. So to speak the language of the new physics we must learn a vocabulary in which process is more important than, and prior to, stasis. Actually there is already available a suitable and very simple language which you will have no trouble understanding.

  From this new point of view, the universe consists of a large number of events. An event may be thought of as the smallest part of a process, a smallest unit of change. But do not think of an event as a change happening to an otherwise static object. It is just a change, no more than that.

  The universe of events is a relational universe. That is, all its properties are described in terms of relationships between the events. The most important relationship that two events can have is causality. This is the same notion of causality that we found was essential to make sense of stories. We say that an event, let us call it A, is in part the cause of another event, B, if A was necessary for B to occur. If A had not occurred, B could not have. In this case we can say that A was a contributing cause of the event B. An event may have more than one contributing cause, and an event may also contribute to causing more than one future event.

  Given any two events, A and B, there are only three possibilities: either A is a cause of B, or B is a cause of A, or neither is the cause of the other. We say that in the first case A is in the causal past of B, in the second, B is in the causal past of A, and in the
third case neither is in the causal past of the other. This is illustrated in Figure 6, in which each event is indicated by a point and each arrow represents a causal relation. Such a picture is a picture of the universe as a process. Figure 7 shows a more complicated universe, consisting of many events, with a complicated set of causal relationships. These pictures are stories told visually - diagrams of the history of a universe.

  Such a universe has time built into it from the beginning. Time and change are not optional, for the universe is a story and it is composed of processes. In such a world, time and causality are synonymous. There is no meaning to the past of an event except the set of events that caused it. And there is no meaning to the future of an event except the set of events it will influence. When we are dealing with a causal universe, we can therefore shorten ‘causal past’ and ‘causal future’ to simply ‘past’ and ‘future’. Figure 8 shows the causal past and future of a particular event in Figure 7. A causal universe is not a series of stills following on, one after the other. There is time, but there is not really any notion of a moment of time. There are only process that follow one another by causal necessity. It makes no sense to say what such a universe is. If one wants to talk about it, one has no alternative but to tell its story.

  FIGURE 6

  The three possible causal relations between two events, A and B: (a) A is to the future of B; (b) B is to the future of A; (c) A and B are neither to the future nor to the past of each other (though they may have other causal relations, for example both being in the past of event C, as shown).

  FIGURE 7

  One volley in a tennis game, represented by the causal relations of a few of its events.

  One way to think of such a causal universe is in terms of the transfer of information. We can think of the content of each arrow in Figures 6 to 8 as a few bits of information. Each event is then something like a transistor that takes in information from events in its past, makes a simple computation and sends the result to the events in its future. A computation is then a kind of story in which information comes in, is sent from transistor to transistor, and is occasionally sent to the output. If we were to remove the inputs and outputs from modern computers, most of them would continue to run indefinitely. The flow of information around the circuits of a computer constitutes a story in which events are computations and causal processes are just the flow of bits of information from one computation to the next. This leads to a very useful metaphor - the universe as a kind of computer. But it is a computer in which the circuitry is not fixed, but can evolve in time as a consequence of the information flowing through it.

  FIGURE 8

  The future and past of Olga’s second return. Note that Sam being confused is in neither set of events.

  Is our universe such a causal universe? General relativity tells us that it is. The description of the universe given by general relativity is exactly that of a causal universe, because of the basic lesson of relativity theory: that nothing can travel faster than light. In particular, no causal effect and no information can travel faster than light. Keep this in mind, and consider two events in the history of our universe, pictured in Figure 9. Let the first be the invention of rock and roll, which took place perhaps somewhere in Nashville in the 1950s. Let the second be the fall of the Berlin Wall, in 1989. Did the first causally influence the second? One may argue about the political and cultural influence of rock and roll, but what is important is only that the invention of rock and roll certainly had some effect on the events leading to the fall of the Berlin Wall. The people who first climbed the wall in triumph had rock and roll songs in their heads, and so did the functionaries who made the decisions that led to the reunification of Germany. So there was certainly a transfer of information from Nashville in the 1950s to Berlin in 1989.

  FIGURE 9

  The invention of rock and roll was in the causal past of the fall of the Berlin Wall because information was able to travel from the first event to the second.

  So in our universe we define the causal future of some event to consist of all the events that it could send information to, using light or any other medium. Since nothing can travel faster than light, the paths of light rays leaving the event define the outer limits of the causal future of an event. They form what we call the future light cone of an event (Figure 10). We call it a cone because, if we draw the picture so that space has only two dimensions, as in Figure 10, it looks like a cone. The causal past of an event consists of all the events that could have influenced it. The influence must travel from some event in the past at the speed of light or less. So the light rays arriving at an event form the outer boundary of the past of an event, and make up what we call the past light cone of an event. One is pictured in Figure 10. We can see that the structure of the causal relations around any event can be pictured in terms of both the past and future light cones. We

  FIGURE 10

  The past and future light cones of an event, A. The future light cone is made up of the paths of all light signals from A to any event in A’s future. Any event inside the cone is in the future of A, causally, because an influence could travel from A to that event at less than the speed of light. We also see the past light cone of A, which contains all the events that may have influenced A. We also see another event, E, which is in neither the past nor the future of A. The diagram is drawn as if space had two dimensions.

  see from Figure 10 also that there are many other events which lie outside both the past and future light cones of our particular event. These are events that took place so far from our event that light could not have reached it. For example, the birth of the worst poet in the universe, on a planet in a galaxy thirty billion light years from us is, fortunately, outside both our future and past light cones. So in our universe, specifying the paths of all the light rays or, equivalently, drawing the light cones around every event, is a way to describe the structure of all possible causal relations. Together, these relations comprise what we call the causal structure of a universe.

  Many popular accounts of general relativity contain a lot of talk about ‘the geometry of spacetime’. But actually most of that has to do with the causal structure. Almost all of the information needed to construct the geometry of spacetime consists of the story of the causal structure. So not only do we live in a causal universe, but most of the story of our universe is the story of the causal relations among its events. The metaphor in which space and time together have a geometry, called the spacetime geometry, is not actually very helpful in understanding the physical meaning of general relativity. That metaphor is based on a mathematical coincidence that is helpful only to those who know enough mathematics to make use of it. The fundamental idea in general relativity is that the causal structure of events can itself by influenced by those events. The causal structure is not fixed for all time. It is dynamical: it evolves, subject to laws. The laws that determine how the causal structure of the universe grows in time are called the Einstein equations. They are very complicated, but when there are big, slow moving klutzes of matter around, like stars and planets, they become much simpler. Basically, what happens then is that the light cones tilt towards the matter, as shown in Figure 11. (This is what is often described as the curvature, or distortion of the geometry of space and time.) As a result, matter tends to fall towards massive objects. This is, of course, another way of talking about the gravitational force. If matter moves around, then waves travel through the causal structure and the light cones oscillate back and forth, as shown in Figure 12. These are the gravitational waves.

  FIGURE 11

  A massive object such as a star causes the light cones in its vicinity to tip towards it. This has the effect of causing freely falling particles to appear to accelerate towards the object.

  So, Einstein’s theory of gravity is a theory of causal structure. It tells us that the essence of spacetime is causal structure and that the motion of matter is a consequence of alterations in the network of causal relations.
What is left out from the notion of causal structure is any measure of quantity or scale. How many events are contained in the passage of a signal from you to me, when we talk on the telephone? How many events have there been in the whole history of the universe in the past of this particular moment, as you finish reading this sentence? If we knew the answers to these questions, and we also knew the structure of causal relations among the events in the history of the universe, then we would know all of what there is to know about the history of the universe.

  FIGURE 12

  A gravitational wave is an oscillation in the directions in which the light cones point in spacetime. Gravitational waves travel at the speed of light.

  There are two kinds of answer we could give to the question of how many events there are in a particular process. One kind of answer assumes that space and time are continuous. In this case time can be divided arbitrarily finely, and there is no smallest possible unit of time. No matter what we think of, say the passage of an electron across an atom, we can think of things that happen a hundred times faster. Newtonian physics assumes that space and time are continuous. But the world is not necessarily like that. The other possibility is that time comes in discrete bits, which can be counted. The answer to the question of how many events are required to transfer a bit of information over a telephone line will then be a finite number. It may be a very large number, but it still will be a finite number. But if space and time consist of events, and the events are discrete entities that can be counted, then space and time themselves are not continuous. If this is true, one cannot divide time indefinitely. Eventually we shall come to the elementary events, ones which cannot be further divided and are thus the simplest possible things that can happen. Just as matter is composed of atoms, which can be counted, the history of the universe is constructed from a huge number of elementary events.