;
. Whereas one type of curvature is produced by mass, another is produced by momentum, and still another by energy.
Of course, these mathematical equations merely express relationships; and it is impossible to deduce from them alone whether it is mass, momentum and vis viva which produce the respective space-time curvatures, or whether it is these space-time curvatures which arise in some mysterious way and are interpreted by our senses as mass, momentum and vis viva. Eddington, as we know, prefers the second attitude, whereas the majority of thinkers prefer the first.
It is to be noted that if we adopt Eddington’s views, a velocity (say,
), being equivalent to
, appears as a ratio of two of the space-time curvatures; hence the co-presence of two special types of space-time curvature would reveal itself to our consciousness as a velocity. Inasmuch as a velocity implies the passage of time, it would seem as though this mysterious passage might be connected in some way with certain of the space-time curvatures. It would be but a step to assume that our entire perceptual world might eventually be reduced to these curvatures. We do not insist on this aspect of the question, first, because we are not certain that they correspond to Eddington’s views, and, secondly, because the theory of relativity has, thus far at least, been unable to interpret electromagnetic phenomena in terms of space-time curvatures.
But there is an interesting idea that Eddington suggests in his book, “Space, Time and Gravitation.” He argues that we are now in a position to understand why it is that velocity is always relative, that is to say, is meaningless otherwise than in relationship to matter. The fact is that the curvatures of space-time, such as