Page:Eddington A. Space Time and Gravitation. 1920.djvu/108

92 with moving particles, light-waves, or material clocks and measuring-rods; hence, without further definition, any geometry of the interior, or any statement about space and time in the interior, is meaningless. But in common life, and frequently in physics, we are not concerned with this microscopic structure of matter. We need to know, not the actual values of the $$g$$'s at a point, but their average values through a region, small from the ordinary standpoint but large compared with the molecular structure of matter. In this macroscopic treatment molecular matter is replaced by continuous matter, and uncurved space-time studded with holes is replaced by an equivalent fully curved space-time without holes. It is natural that our senses should have developed faculties for perceiving some of these intrinsic distinctions of the possible states of the world around us. I prefer to think of matter and energy, not as agents causing the degrees of curvature of the world, but as parts of our perceptions of the existence of the curvature.

It will be seen that the law of gravitation can be summed up in the statement that in an empty region space-time can be curved only in the first degree.