7 - What can geometry explain?

Summary

Introduction

If space and spacetime are explanatory ideas in physics and common sense, just what sort of explanation do they offer? This question can't be answered until we have a clear idea of what kinds of states, events and processes we might be able to explain by making use of space and its structures – of geometry, in short. It is not obvious that space does have any significant role in explanation, but perhaps this can be made more obvious by exercising our imaginations about how things would be and what would explain them if space were very different from the way we find it. Part of this essay considers that question.

There is a central question about whether explanations which draw on the nature of space are causal or of their own kind. Conversely there is a question whether we can discover what the nature of space or spacetime is unless we find it out by means of the causal influences revealed in what it explains about the fixed properties of things and the occurrences of events. If we look at this question outside the context of GR, which is what I do for most of the essay, there is good reason to reject the tie between what geometry can explain and what we explain by means of causes. There are advantages in a clear sight of this. The situation in GR is more ambiguous and I touch on it only rather briefly.