Page:Eddington A. Space Time and Gravitation. 1920.djvu/154

138 follow it. That is satisfactory, so far as it goes, but still we should naturally wish for a clearer picture of the cause—inertia-gravitation—which propels it in this track.

It has been seen that the gravitational field round a body involves a kind of curvature of space-time, and accordingly round each particle there is a minute pucker. Now at each successive instant a particle is displaced continuously in time if not in space; and so in our four-dimensional representation which gives a bird s-eye-view of all time, the pucker has the form of a long groove along the track of the particle. Now such a groove or pleat in a continuum cannot take an arbitrary course—as every dress-maker knows. Einstein's law of gravitation gives the rule according to which the curvatures at any point of space-time link on to those at surrounding points; so that when a groove is started in any direction the rest of its course can be forecasted. We have hitherto thought of the law of gravitation as showing how the pucker spreads out in space, cf. Newton s statement that the corresponding force weakens as the inverse square of the distance. But the law of Einstein equally shows how the gravitational field spreads out in time, since there is no absolute distinction of time and space. It can be deduced mathematically from Einstein's law that a pucker of the form corresponding to a particle necessarily runs along the track of greatest interval-length between two points.

The track of a particle of matter is thus determined by the interaction of the minute gravitational field, which surrounds and, so far as we know, constitutes it, with the general space-time of the region. The various forms which it can take, find their explanation in the new law of gravitation. The straight tracks of the stars and the curved tracks of the planets are placed on the same level, and receive the same kind of explanation. The one universal law, that the space-time continuum can be curved only in the first degree, is sufficient to prescribe the forms of all possible grooves crossing it.

The application of Einstein's law to trace the gravitational field not only through space but through time leads to a great unification of mechanics. If we have given for a start a narrow slice of space-time representing the state of the universe for a few seconds, with all the little puckers belonging to particles of matter