Einstein's theories of relativity and gravitation; a selection of material from the essays submitted in the competition for the Eugene Higgins prize of 5,000 dollars compiled and edited, and introductory matter supplied by JMalcolm Bird . it is possible for any line on the surface of a sphereto be straight. Hence, all axes must be curved, andall observers, whatever their states of motion, mustexperience fields of force which are of the samenature as those due to motion only. The extra forceexperienced when a lift begins to rise is an exampleof force due to pure motion: gravitation is thesimila
Einstein's theories of relativity and gravitation; a selection of material from the essays submitted in the competition for the Eugene Higgins prize of 5,000 dollars compiled and edited, and introductory matter supplied by JMalcolm Bird . it is possible for any line on the surface of a sphereto be straight. Hence, all axes must be curved, andall observers, whatever their states of motion, mustexperience fields of force which are of the samenature as those due to motion only. The extra forceexperienced when a lift begins to rise is an exampleof force due to pure motion: gravitation is thesimilar force due to an inherent curvature of thefour-space, and it was the postulate that these forceswere similar that made possible Einsteins solutionof the general problem of gravitation. The Time Diagram The correlation of time with its geometrical ana-logue is of absorbing interest. Representing velocityby the common method of plotting a curve showingpositions at various times and marking distanceshorizontally and times vertically, the velocity of 274 RELATIVITY AND GRAVITATION light being i, MM and NN will both representthis velocity. Since this is assumed to be the greatestvelocity occurring in nature, all other possible veloci-. ties are represented by lines falling within the upperand lower Vs. Now this diagram correctly repre-sents two dimensions of Minkowskis Euclideanfour-space so, transmuting to real but flat four-spaceby multiplying times by V— i, it Is seen that thereis a region outside which no effect can be propagatedfrom O since that would Involve the existence of avelocity greater than that of light. This regionrepresents the future of O. Similarly, O can onlybe affected by events within the region derived fromthe downward-opening V, which therefore representsthe past of O. The region between the two rep-resents events which may be either simultaneous THE NEW WORLD 275 with O or not, according to the velocity of the ob-server at O. Thus in this theory an event d
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