Three Roads to Quantum Gravity Read Online Free Page B

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