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Temporal separation between two events. Events A and B occur with the following spacetime coordinates in the reference frames of Fig. 37-25: according to the unprimed frame, (xA, tA) and (xB, 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.
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