Page:Eddington A. Space Time and Gravitation. 1920.djvu/192

176 be found out by exploration with an uncharged particle. Actually we prefer to look at the world as revealed by exploration with scales and clocks—the former for measuring so-called imaginary intervals, and the latter for real intervals; this gives us a unified geometrical conception of the world. Presumably, we could obtain a unified mechanical conception by taking the moving uncharged particle as standard indicator; or a unified electrical conception by taking the charged particle. For particular purposes one test-body is generally better adapted than others. The gravitational field is more sensitively explored with a moving particle than a scale. Although the electrical field can theoretically be explored by the change of length of a scale taken round a circuit, a far more sensitive way is to use a little bit of the scale—an electron. And in general for practical efficiency, we do not use any simple type of apparatus, but a complicated construction built up with a view to a particular experiment. The reason for emphasising the theoretical interchangeability of test-bodies is that it brings out the unity and simplicity of the world; and for that reason there is an importance in characterising the electromagnetic condition of the world by reference to the indications of a scale and clock, however inappropriate they may be as practical test-bodies.

Weyl's theory opens up interesting avenues for development. The details of the further steps involve difficult mathematics; but a general outline is possible. As on Einstein's more limited theory there is at any point an important property of the world called the curvature; but on the new theory it is not an absolute quantity in the strictest sense of the word. It is independent of the observer's mesh-system, but it depends on his gauge. It is obvious that the number expressing the radius of curvature of the world at a point must depend on the unit of length; so we cannot say that the curvatures at two points are absolutely equal, because they depend on the gauges assigned at the two points. Conversely the radius of curvature of the world provides a natural and absolute gauge at every point; and it will presumably introduce the greatest possible symmetry into our laws if the observer chooses this, or some definite fraction of it, as his gauge. He, so to speak, forces the world to be spherical by adopting at every point a unit of length which will make it so.