Page:The principle of relativity (1920).djvu/153

 Because the sense of the postulate is that the four-dimensional world is given in space and time by phenomena only, but the projection in time and space can be handled with a certain freedom, and therefore I would rather like to give to this assertion the name "The Postulate of the Absolute world" [World-Postulate].

III

By the world-postulate a similar treatment of the four determining quantities x, y, z, t, of a world-point is possible. Thereby the forms under which the physical laws come forth, gain in intelligibility, as I shall presently show. Above all, the idea of acceleration becomes much more striking and clear.

I shall again use the geometrical method of expression. Let us call any world-point O as a "Space-time-null-point." The cone

c^2t^2 - x^2 - y^2 - z^2 = O

consists of two parts with O as apex, one part having t < 0´, the other having t > 0. The first, which we may call the fore-cone consists of all those points which send light towards O, the second, which we may call the aft-cone. consists of all those points which receive their light from O. The region bounded by the fore-cone may be called the fore-side of O, and the region bounded by the aft-cone may be called the aft-side of O. (Vide fig. 2).

On the aft-side of O we have the already considered hyperboloidal shell F = c^2t - x^2 - y^2 - z^2 = 1, t > 0.