By Richard T. Weidner and Robert L. Sells
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Thesirnunaneaus birfhs [a) d Jim. John, snd Dick. as observed in system S , and (b) of Jim and Dick, us observed #nsvsfern S,. /oh> to be 49 years old and 2 light-yr from Jim and Dick. See Table 2- 7. CHAP. 2 Relativistic Kinematics: Space end Time somewhere between 0 and 1. In our problem of the earth and the rocket ship there are six relevant events: the birth and death of Jim, the birth and death of John, and the birth and death of Dick. If we know the space-time coordinates of an event as observed in one of the systems, we can use (2-24) to obtain the coordinates of the same event as observed in the other system.
Thus, it is not essential that the spatial measurements be made simultaneously in the system in which the object is at rest. Using (2-24), we have with ti = t l . The length of Sz's meterstick, as measured by S2, is xi - x2 = Lo;the length of this same meterstick, moving at speed v with respect to system S1, but now as measured by S1, is xi - x, = L. Therefore, (2-26) becomes CHAP. 2 Relefivistic Kinematics: Space end Time This relation shows the phenomenon of space contraction. Measuring the length of Sz's moving meterstick, S , finds it to be contracted by a ] " ~ the direction of the relative motion.
000 muons approachinp narlh. (b) 500 undecs yed muons arnving 8t aenh. 000 muons, ( d ) esrth arriving rrr 500 undeca yed muons. Len* Yl ~d Tima Intmmmh in RmiYiiwity PbydCI . SEC. 446 km. 52 x lo-* a. But this ia just the decay half-life in the rest system of the muons; therefore, an obseroer in that system also will find500 of the original 1,000muons surviving when the earth reaches the muons. Although the two observers, one on earth and one with the muons, disagree on the measurements of time and of Iength intervals, they both agree that 500 muons survjve when the earth and muons meet.