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APPENDIX

75

that time and space shall reduce to mere shadows and we shall have a world complete in itself.


II

Now the question may be asked, — what circumstances lead us to these changed views about time and space, are they not in contradiction with observed phenomena, do they finally guarantee us advantages for the description of natural phenomena?

Before we enter into the discussion, a very important point must be noticed. Suppose we have individualised time and space in any manner; then a world-line parallel to the t-axis will correspond to a stationary point; a world-line inclined to the t-axis will correspond to a point moving uniformly; and a world-curve will correspond to a point moving in any manner. Let us now picture to our mind the world-line passing through any world point x, y, z, t; now if we find the world-line parallel to the radius vector OA' of the hyperboloidal sheet, then we can introduce OA' as a new time-axis, and then according to the new conceptions of time and space the substance will appear to be at rest in the world point concerned. We shall now introduce this fundamental axiom: —

The substance existing at any world point can always be conceived to he at rest, if we establish our time and space suitably. The axiom denotes that in a world-point the expression

shall always be positive or what is equivalent to the same thing, every velocity V should be smaller than c. c shall therefore be the upper limit for all substantial velocities and herein lies a deep significance for the