Page:Eddington A. Space Time and Gravitation. 1920.djvu/211

of the world-structure or aether, where the $T_{\mu \nu }$ vanish, is always of the indeterminate form 0 ÷ 0. On the other hand acceleration and rotation are defined by means of the $g_{\mu \nu }$ and exist wherever these exist^[1]; so that the acceleration and rotation of the world-structure or aether relative to the frame of reference are determinate. Notice that acceleration is not defined as change of velocity; it is an independent entity, much simpler and more universal than velocity. It is from a comparison of these two entities that we ultimately obtain the definition of time.

This finally resolves the difficulty encountered in Chapter x—the apparent difference in the Principle of Relativity as applied to uniform and non-uniform motion. Fundamentally velocity and acceleration are both static qualities of a region of the world (referred to some mesh-system). Acceleration is a comparatively simple quality present wherever there is geodesic structure, that is to say everywhere. Velocity is a highly complex quality existing only where the structure is itself more than ordinarily complicated, viz. in matter. Both these qualities commonly give physical manifestations, to which the terms acceleration and velocity are more particularly applied; but it is by examining their more fundamental meaning that we can understand the universality of the one and the localisation of the other.

It has been shown that there are four identical relations between the ten qualities of a piece of matter here identified, which depend solely on the way the $G_{\mu \nu }$ were by definition constructed out of simpler elements. These four relations state that, provided the mesh-system is drawn in one of a certain number of ways, mass (or energy) and momentum will be conserved. The conservation of mass is of great importance; matter will be permanent, and for every particle disappearing at any point a corresponding mass will appear at a neighbouring point; the change consists in the displacement of matter, not its creation or destruction. This gives matter the right to be regarded, not as a mere assemblage of symbols, but as the substance of a

1. Even in Newtonian mechanics we speak of the "field of acceleration," and think of it as existing even when there is no test body to display the acceleration. In the present theory this field of acceleration is described by the $g_{\mu \nu }$. There is no such thing as a "field of velocity" in empty space; but there is in a material ocean.