Chapter 37, Problem 60P

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, (x_A, t_A) and (x_B, t_B); according to the primed frame, (x'_A, t'_A) and (x'_B, t'_B). In the unprimed frame, ∆t= t_B − t_A = 1.00 µs and ∆x = x_B − x_A = 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.