. Space, time and gravitation : an outline of the general relativity theory. wing BC in thedirection of the velocity of m2, prolonged through threetime-partitions, the horizontal progress from B represents themomentum of the second particle. The length PC then repre-sents the total momentum of the system of two particles. Suppose that some change of their velocities occurs, notinvolving any transference of momentum from outside, acollision. Since the total momentum PC is unaltered, a similar ix] MOMENTUM AND ENERGY 143 construction made with the new velocities must again bring usto C; tha
. Space, time and gravitation : an outline of the general relativity theory. wing BC in thedirection of the velocity of m2, prolonged through threetime-partitions, the horizontal progress from B represents themomentum of the second particle. The length PC then repre-sents the total momentum of the system of two particles. Suppose that some change of their velocities occurs, notinvolving any transference of momentum from outside, acollision. Since the total momentum PC is unaltered, a similar ix] MOMENTUM AND ENERGY 143 construction made with the new velocities must again bring usto C; that is to say, the new velocities are represented by thedirections OB, BC, where B is some other point on the line examine how this will appear to some other observer Stin uniform motion relative to S. His transformation of spaceand time has been described in Chapter in and is represented inFig. 20, which shows how his time-partitions run as comparedwith those of S. The same actual motion is, of course, repre-sented by parallel directions in the two diagrams; but the. Fig. 20. interpretation as a velocity MA is different in the two the velocity of m1 through two time-partitions, and ofra2 through three time-partitions, as before, we find that the totalmomentum for the observer St is represented by PC (Fig. 20);but making a similar construction with the velocities aftercollision, we arrive at a different point C. Thus whilst momen-tum is conserved for the observer S, it has altered from PC toPC for the observer Sx. The discrepancy arises because in the construction the linesare prolonged to meet partitions which are different for the two 144 MOMENTUM AND ENERGY [ch. observers. The rule for determining momentum ought to besuch that both observers make the same construction, inde-pendent of their partitions, so that both arrive by the two routesat the same point C. Then it will not matter if, through theirdifferent measures of time, one observer measures moment
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