Three Roads to Quantum Gravity by Lee Smolin

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.
    What we already know about quantum gravity suggests that the second possibility is right. The apparent smoothness of space and time are illusions; behind them is a world composed of discrete sets of events, which can be counted. Different approaches give us different pieces of evidence for this conclusion, but they all agree that if we looks finely enough at our world the continuity of space and time will dissolve as surely as the smoothness of material gives way to the discrete world of molecules and atoms.
    The different approaches also agree about how far down we have to probe the world before we come to the elementary events. The scales of time and distance on which the discrete structure of the world becomes manifest is called the Planck scale. It is defined as