Three Roads To Quantum Gravity

22 THREE ROADS TO QUANTUM GRAVITY
In fact, these relationships are all there is to the gravitational
®eld. Two sets of ®eld lines that link and knot in the
same way de®ne 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.
FIGURE 2
The gravitational ®eld is like the electric ®eld but requires three sets of ®eld
lines to describe it.
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 ®eld lines.
This is one of the important differences between general
relativity and other theories such as electromagnetism. In the
theory of electric ®elds it is assumed that points have meaning.
It makes sense to ask in which direction the ®eld lines
pass at a given point. Consequently, two sets of electric ®eld
lines that differ only in that one is moved a metre to the left, as