the mass of attracting matter needed to produce it. On the other hand, the earth's absolute acceleration does not intrude on our attention in the way that its absolute rotation does[1].
We are vaguely conscious of a difficulty in these results; but if we examine it closely, the difficulty does not seem to be a very serious one. The theory of relativity, as we have understood it, asserts that our partitions of space and time are introduced by the observer and are irrelevant to the laws of nature; and therefore the current quantities of physics, length, duration, mass, force, etc., which are relative to these partitions, are not things having an absolute significance in nature. But we have never denied that there are features of the world having an absolute significance; in fact, we have spent much time in finding such features. The geodesics or natural tracks have been shown to have an absolute significance; and it is possible in a limited region of the world to choose space and time partitions such that all geodesics become approximately straight lines. We may call this a "natural" frame for that region, although it is not as a rule the space and time adopted in practice; it is for example the space and time of the observers in the falling projectile, not of Newton's super-observer. It is capable of absolute definition, except that it is ambiguous in regard to uniform motion. Now the rotation of the earth determined by Foucault's pendulum experiment is the rotation referred to this natural frame. But we must have misunderstood our own theory of relativity altogether, if we think there is anything inadmissible in an absolute rotation of such a kind.
Material particles and geodesics are both features of the absolute structure of the world; and a rotation relative to geodesic structure does not seem to be on any different footing from a velocity relative to matter. There is, however, the striking feature that rotation seems to be relative not merely to the local geodesic structure but to a generally accepted universal frame; whereas it is necessary to specify precisely
- ↑ To determine even roughly the earth's absolute acceleration we should need a fairly full knowledge of the disturbing effects of all the matter in the universe. A similar knowledge would be required to determine the absolute rotation accurately; but all the matter likely to exist would have so small an effect, that we can at once assume that the absolute rotation is very nearly the same as the experimentally determined rotation.
