CHAPTER XI
ELECTRICITY AND GRAVITATION
Thou shalt not have in thine house divers measures, a great and a small.
But thou shalt have a perfect and just weight, a perfect and just measure shalt thou have.
The relativity theory deduces from geometrical principles the existence of gravitation and the laws of mechanics of matter. Mechanics is derived from geometry, not by adding arbitrary hypotheses, but by removing unnecessary assumptions, so that a geometer like Riemann might almost have foreseen the more important features of the actual world. But nature has in reserve one great surprise—electricity.
Electrical phenomena are not in any way a misfit in the relativity theory, and historically it is through them that it has been developed. Yet we cannot rest satisfied until a deeper unity between the gravitational and electrical properties of the world is apparent. The electron, which seems to be the smallest particle of matter, is a singularity in the gravitational field and also a singularity in the electrical field. How can these two facts be connected? The gravitational field is the expression of some state of the world, which also manifests itself in the natural geometry determined with measuring appliances; the electric field must also express some state of the world, but we have not as yet connected it with natural geometry. May there not still be unnecessary assumptions to be removed, so that a yet more comprehensive geometry can be found, in which gravitational and electrical fields both have their place?
There is an arbitrary assumption in our geometry up to this point, which it is desirable now to point out. We have based everything on the "interval," which, it has been said, is some thing which all observers, whatever their motion or whatever their mesh-system, can measure absolutely, agreeing on the result. This assumes that they are provided with identical standards of measurement—scales and clocks. But if is in
