Three Roads To Quantum Gravity

54 THREE ROADS TO QUANTUM GRAVITY
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 ®rst 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 in¯uence. 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
A
B
C
A
B
B
A
(a) (b) (c)
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).