APPENDIX

85

From the very beginning, we can establish the ratio between the units of time and space in such a manner, that the velocity of light becomes unity. If we now write , in the place of *t*, then the differential expression

becomes symmetrical in (*x, y, z, l*); this symmetry then enters into each law, which does not contradict the *world-postulate*. We can clothe the essential nature of this postulate in the mystical, but mathematically significant formula

^{5}km = Sec.

V

The advantages arising from the formulation of the world-potulate are illustrated by nothing so strikingly as by the expressions which tell us about the reactions exerted by a point-charge moving in any manner according to the Maxwell-Lorentz theory.

Let us conceive of the world-line of such an electron with the charge (*e*), and let us introduce upon it the "Proper-time" τ reckoned from any possible initial point. In order to obtain the field caused by the electron at any world-point P_{1} let us construct the fore-cone belonging to P_{1} (*vide* fig. 4). Clearly this cuts the unlimited world-line of the electron at a single point P, because these directions are all time-like vectors. At P, let us draw the tangent to the world-line, and let us draw from P_{1} the normal to this tangent. Let *r* be the measure of P_{1}Q. According to the definition of a fore-cone, *r/c* is to be reckoned as the measure of PQ. Now at the world-point P_{1},