Chapter One THERE IS NOTHING OUTSIDE THE UNIVERSE We humans are the species that makes things. So when we find something that appears to be beautifully and intricately structured, our almost instinctive response is to ask, `Who made that?' The most important lesson to be learned if we are to prepare ourselves to approach the universe scientifically is that this is not the right question to ask. It is true that the universe is as beautiful as it is intricately structured. But it cannot have been made by anything that exists outside it, for by definition the universe is all there is, and there can be nothing outside it. And, by definition, neither can there have been anything before the universe that caused it, for if anything existed it must have been part of the universe. So the first principle of cosmology must be `There is nothing outside the universe'. This is not to exclude religion or mysticism, for there is always room for those sources of inspiration for those who seek them. But if it is knowledge we desire, if we wish to understand what the universe is and how it came to be that way, we need to seek answers to questions about the things we see when we look around us. And the answers can involve only things that exist in the universe. This first principle means that we take the universe to be, by definition, a closed system. It means that the explanation for anything in the universe can involve only other things that also exist in the universe. This has very important consequences, each of which will be reflected many times in the pages that follow. One of the most important is that the definition or description of any entity inside the universe can refer only to other things in the universe. If something has a position, that position can be defined only with respect to the other things in the universe. If it has a motion, that motion can be discerned only by looking for changes in its position with respect to other things in the universe. So, there is no meaning to space that is independent of the relationships among real things in the world. Space is not a stage, which might be either empty or full, onto which things come and go. Space is nothing apart from the things that exist; it is only an aspect of the relationships that hold between things. Space, then, is something like a sentence. It is absurd to talk of a sentence with no words in it. Each sentence has a grammatical structure that is defined by relationships that hold between the words in it, relationships like subject-object or adjective-noun. If we take out all the words we are not left with an empty sentence, we are left with nothing. Moreover, there are many different grammatical structures, catering for different arrangements of words and the various relationships between them. There is no such thing as an absolute sentence structure that holds for all sentences independent of their particular words and meanings. The geometry of a universe is very like the grammatical structure of a sentence. Just as a sentence has no structure and no existence apart from the relationships between the words, space has no existence apart from the relationships that hold between the things in the universe. If you change a sentence by taking some words out, or changing their order, its grammatical structure changes. Similarly, the geometry of space changes when the things in the universe change their relationships to one another. As we understand it now, it is simply absurd to speak of a universe with nothing in it. That is as absurd as a sentence with no words. It is even absurd to speak of a space with only one thing in it, for then there would be no relationships to define where that one thing is. (Here the analogy breaks down because there do exist sentences of one word only. However, they usually get their meaning from their relationships with adjacent sentences.) The view of space as something that exists independent of any relationships is called the absolute view. It was Newton's view, but it has been definitively repudiated by the experiments that have verified Einstein's theory of general relativity. This has radical implications, which take a lot of thinking to get used to. There are unfortunately not a few good professional physicists who still think about the world as if space and time had an absolute meaning. Of course, it does seem as though the geometry of space is not affected by things moving around. When I walk from one side of a room to the other, the geometry of the room does not seem to change. After I have crossed the room, the space within it still seems to satisfy the rules of Euclidean geometry that we learned in school, as it did before I started to move. Were Euclidean geometry not a good approximation to what we see around us, Newton would not have had a chance. But the apparent Euclidean geometry of space turns out to be as much an illusion as the apparent flatness of the Earth. The Earth seems flat only when we can't see the horizon. Whenever we can see far enough, from an aircraft or when we gaze out to sea, we can easily see that this is mistaken. Similarly, the geometry of the room you are in seems to satisfy the rules of Euclidean geometry only because the departures from those rules are very small. But if you could make very precise measurements you would find that the angles of triangles in your room do not sum to exactly 180 degrees. Moreover, the sum actually depends on the relation of the triangle to the stuff in the room. If you could measure precisely enough you would see that the geometries of all the triangles in the room do change when you move from one side of it to the other. It may be that each science has one main thing to teach humanity, to help us shape our story of who we are and what we are doing here. Biology's lesson is natural selection, as its exponents such as Richard Dawkins and Lynn Margulis have so eloquently taught us. I believe that the main lesson of relativity and quantum theory is that the world is nothing but an evolving network of relationships. I have not the eloquence to be the Dawkins or Margulis of relativity, but I do hope that after reading this book you will have come to understand that the relational picture of space and time has implications that are as radical as those of natural selection, not only for science but for our perspective on who we are and how we came to exist in this evolving universe of relations. Charles Darwin's theory tells us that our existence was not inevitable, that there is no eternal order to the universe that necessarily brought us into being. We are the result of processes much more complicated and unpredictable than the small aspects of our lives and societies over which we have some control. The lesson that the world is at root a network of evolving relationships tells us that this is true to a lesser or greater extent of all things. There is no fixed, eternal frame to the universe to define what may or may not exist. There is nothing beyond the world except what we see, no background to it except its particular history. This relational view of space has been around as an idea for a long time. Early in the eighteenth century, the philosopher Gottfried Wilhelm Leibniz argued strongly that Newton's physics was fatally flawed because it was based on a logically imperfect absolute view of space and time. Other philosophers and scientists, such as Ernst Mach, working in Vienna at the end of the nineteenth century, were its champions. Einstein's theory of general relativity is a direct descendent of these views. A confusing aspect of this is that Einstein's theory of general relativity can consistently describe universes that contain no matter. This might lead one to believe that the theory is not relational, because there is space but there is no matter, and there are no relationships between the matter that serve to define space. But this is wrong. The mistake is in thinking that the relationships that define space must be between material particles. We have known since the middle of the nineteenth century that the world is not composed only of particles. A contrary view, which shaped twentieth-century physics, is that the world is also composed of fields. Fields are quantities that vary continuously over space, such as electric and magnetic fields. The electric field is often visualized as a network of lines of force surrounding the object generating the field, as shown in Figure 1. What makes this a field is that there is a line of force passing through every point (as with a contour map, only lines at certain intervals are depicted). If we were to put a charged particle at any point in the field, it would experience a force pushing it along the field line that goes through that point. General relativity is a theory of fields. The field involved is called the gravitational field. It is more complicated than the electric field, and is visualized as a more complicated set of field lines. It requires three sets of lines, as shown in Figure 2. We may imagine them in different colours, say red, blue and green. Because there are three sets of field lines, the gravitational field defines a network of relationships having to do with how the three sets of lines link with one another. These relationships are described in terms of, for example, how many times one of the three kinds of line knot around those of another kind. In fact, these relationships are all there is to the gravitational field. Two sets of field lines that link and knot in the same way define the same set of relationships, and exactly the same physical situation (an example is shown in Figure 3). This is why we call general relativity a relational theory. Points of space have no existence in themselves -- the only meaning a point can have is as a name we give to a particular feature in the network of relationships between the three sets of field lines. This is one of the important differences between general relativity and other theories such as electromagnetism. In the theory of electric fields it is assumed that points have meaning. It makes sense to ask in which direction the field lines pass at a given point. Consequently, two sets of electric field lines that differ only in that one is moved a metre to the left, as in Figure 4, are taken to describe different physical situations. Physicists using general relativity must work in the opposite way. They cannot speak of a point, except by naming some features of the field lines that will uniquely distinguish that point. All talk in general relativity is about relationships among the field lines. One might ask why we do not just fix the network of field lines, and define everything with respect to them. The reason is that the network of relationships evolves in time. Except for a small number of idealized examples which have nothing to do with the real world, in all the worlds that general relativity describes the networks of field lines are constantly changing. This is enough for the moment about space. Let us turn now to time. There the same lesson holds. In Newton's theory time is assumed to have an absolute meaning. It flows, from the infinite past to the infinite future, the same everywhere in the universe, without any relation to things that actually happen. Change is measured in units of time, but time is assumed to have a meaning and existence that transcends any particular process of change in the universe. In the twentieth century we learned that this view of time is as incorrect as Newton's view of absolute space. We now know that time also has no absolute meaning. There is no time apart from change. There is no such thing as a clock outside the network of changing relationships. So one cannot ask a question such as how fast, in an absolute sense, something is changing: one can only compare how fast one thing is happening with the rate of some other process. Time is described only in terms of change in the network of relationships that describes space. This means that it is absurd in general relativity to speak of a universe in which nothing happens. Time is nothing but a measure of change -- it has no other meaning. Neither space nor time has any existence outside the system of evolving relationships that comprises the universe. Physicists refer to this feature of general relativity as background independence . By this we mean that there is no fixed background, or stage, that remains fixed for all time. In contrast, a theory such as Newtonian mechanics or electromagnetism is background dependent because it assumes that there exists a fixed, unchanging background that provides the ultimate answer to all questions about where and when. One reason why it has taken so long to construct a quantum theory of gravity is that all previous quantum theories were background dependent. It proved rather challenging to construct a background independent quantum theory, in which the mathematical structure of the quantum theory made no mention of points, except when identified through networks of relationships. The problem of how to construct a quantum theoretic description of a world in which space and time are nothing but networks of relationships was solved over the last 15 years of the twentieth century. The theory that resulted is loop quantum gravity, which is one of our three roads. I shall describe what it has taught us in Chapter 10. Before we get there, we shall have to explore other implications of the principle that there is nothing outside the universe. Excerpted from THREE ROADS TO QUANTUM GRAVITY by LEE SMOLIN. Copyright © 2001 by Lee Smolin. Excerpted by permission. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
