Substantival spacetime

Newtonian space is both substantival and absolute: able to exist in the absence of matter, possessed of an immutable Euclidean geometry, it is entirely unaffected by the presence and distribution of matter within it. The spacetime of gtr is very different; its geometry is variable, and affected by the presence and activities of material things. gtr's spacetime is certainly not absolute, but is it substantival? Einstein certainly came to think it was. In his 1920 Leyden lecture “Ether and the theory of relativity” he remarked that the theory “has, I think, finally disposed of the view that space is physically empty” (1922: 18). It is not hard to see why he adopted this view.

We saw in §14.2 and §14.3 that in variably curved spaces – for example, worlds where non-Euclidean “holes” occur at irregular intervals – the relationist faces a near-impossible task in seeking to explain the behaviour of bodies solely in terms of object-object forces and relations. Since the internal tensions suffered by a body moving through such a hole cannot be explained by alterations in the shape of space, they must be explained in terms of relations between the body in question and other bodies; since the other bodies may be in any number of different configurations, the laws involved – if it proves possible to formulate any – will be horrendously complex.

Since, according to gtr, variations in the geometry of spacetime are related to the movements of matter, areas of strong localized curvature sitting motionless in empty tracts of spacetime are unlikely to be encountered.