Temporal separation between two events. Events A and B occur with the following spacetime coordinates in the reference frames of Fig.37-26: according to the unprimed frame, (xA, tA) and (x’B, tB); according to the primed frame, (x’A, t’A) and (x’B,t’B).In the unprimed frame, ?t = tB - tA = 1.00 µs and ?x = xB = xA = 240 m. (a) Find an expression for ?t’ in terms of the speed parameter β and the given data. Graph ?t’ versus β for the following two ranges of β: (b) 0 to 0.01 and (c) 0.1 to 1. (d) At what value of β is ?t\" minimum and (e) what is that minimum? (f) Can one of these events cause the other? Explain.
Fig. 37-26
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