Page:Eddington A. Space Time and Gravitation. 1920.djvu/206

190 with his indefinable intervals and point-events. He has arrived at the quantity $$G_{\mu\nu}$$; but as yet this means to us—absolutely nothing. The pure mathematician left to himself never "deviates into sense." His work can never relate to the familiar things around us, unless we boldly lay hold of some of his symbols and give them an intelligible meaning—tentatively at first, and then definitely as we find that they satisfy all experimental knowledge. We have decided that in empty space $$G_{\mu\nu}$$ vanishes. Here is our opportunity. In default of any other suggestion as to what the vanishing of $$G_{\mu\nu}$$ might mean, let us say that the vanishing of $$G_{\mu\nu}$$ means emptiness; so that $$G_{\mu\nu}$$, if it does not vanish, is a condition of the world which distinguishes space said to be occupied from space said to be empty. Hitherto $$G_{\mu\nu}$$ was merely a formal outline to be filled with some undefined contents; we are as far as ever from being able to explain what those contents are; but we have now given a recognisable meaning to the completed picture, so that we shall know it when we come across it in the familiar world of experience.

The two equations are accordingly merely definitions—definitions of the way in which certain states of the world (described in terms of the indefinables) impress themselves on our perceptions. When we perceive that a certain region of the world is empty, that is merely the mode in which our senses recognise that it is curved no higher than the first degree. When we perceive that a region contains matter we are recognising the intrinsic curvature of the world; and when we believe we are measuring the mass and momentum of the matter (relative to some axes of reference) we are measuring certain components of world-curvature (referred to those axes). The statistical averages of something unknown, which have been used to describe the state of the world, vary from point to point; and it is out of these that the mind has constructed the familiar notions of matter and emptiness.

The law of gravitation is not a law in the sense that it restricts the possible behaviour of the substratum of the world; it is merely the definition of a vacuum. We need not regard matter as a foreign entity causing a disturbance in the gravitational field; the disturbance is matter. In the same way we do not regard light as an intruder in the electromagnetic field, causing