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 . th appropriate conven-tions, either may stand as the mental picture of theexternal world; it is lor us to choose which is themore convenient and useful image. Einstein tells usthat his image is the better, and tells us why. Before we look into this, we must let him tell ussomething more about the geometry of his con-tinuum. What he tells us is, in its essenti
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 . th appropriate conven-tions, either may stand as the mental picture of theexternal world; it is lor us to choose which is themore convenient and useful image. Einstein tells usthat his image is the better, and tells us why. Before we look into this, we must let him tell ussomething more about the geometry of his con-tinuum. What he tells us is, in its essentials, just THE SPACE-TIME CONTINUUM 163 this. The observer in a pure space continuum ofthree dimensions finds that as he changes his position,his right-and-left, his backward-and-forward, andhis up-and-down are not fixed directions inherentin nature, but are fully interchangeable. The ob-servers, in the adjoined sketch, whose verticals areas indicated by the arrows, find very different ver-tical and horizontal components for the distancebetween the points O and P; a similar situationwould prevail if we used all three space statement analogous to this for Einsteins four-dimensional continuum of space and time combined. is that, as observers change their relative motion,their time axes take slightly different directions, sothat what is purely space or purely time for theone becomes space with a small component in thetime direction, or time with a small component in thespace direction, for the other. This it will be seenexplains fully why observers in relative motion can 164 RELATIVITY AND GRAVITATION differ about space and time measurements. Weshould not be at all surprised If the two observersof the figure reported different values for horizontalsand verticals; we should realize that what was ver-tical for one had become partly horizontal for theother. It Is just so, says Einstein, with his ob-servers of time and space who are In relative motionto one another; what
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