Free Three Roads to Quantum Gravity by Lee Smolin Page B

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