Page:Eddington A. Space Time and Gravitation. 1920.djvu/207

XII] the electromagnetic force to oscillate along its path; the oscillations constitute the light. Nor is heat a fluid causing agitation of the molecules of a body; the agitation is heat.

This view, that matter is a symptom and not a cause, seems so natural that it is surprising that it should be obscured in the usual presentation of the theory. The reason is that the connection of mathematical analysis with the things of experience is usually made, not by determining what matter is, but by what certain combinations of matter do. Hence the interval is at once identified with something familiar to experience, namely the thing that a scale and a clock measure. However advantageous that may be for the sake of bringing the theory into touch with experiment at the outset, we can scarcely hope to build up a theory of the nature of things if we take a scale and clock as the simplest unanalysable concepts. The result of this logical inversion is that by the time the equation $$G_{\mu\nu} = K_{\mu\nu}$$ is encountered, both sides of the equation are well-defined quantities. Their necessary identity is overlooked, and the equation is regarded as a new law of nature. This is the fault of introducing the scale and clock prematurely. For our part we prefer first to define what matter is in terms of the elementary concepts of the theory; then we can introduce any kind of scientific apparatus; and finally determine what property of the world that apparatus will measure.

Matter defined in this way obeys all the laws of mechanics, including conservation of energy and momentum. Proceeding with a similar development of Weyl's more general theory of the combined gravitational and electrical fields, we should find that it has the familiar electrical and optical properties. It is purely gratuitous to suppose that there is anything else present, controlling but not to be identified with the relations of the fourteen potentials ($$g$$'s and $$k$$'s).

There is only one further requirement that can be demanded from matter. Our brains are constituted of matter, and they feel and think—or at least feeling and thinking are closely associated with motions or changes of the matter of the brain. It would be difficult to say that any hypothesis as to the nature of matter makes this process less or more easily understood; and a brain constituted out of differential coefficients of $$g$$'s can