Chapter 37, Problem 21P

Relativistic reversal of events. Figures 37-25a and b show the (usual) situation in which a primed reference frame passes an un-primed reference frame, in the common positive direction of the x and x' axes, at a constant relative velocity of magnitude v. We are at rest in the unprimed frame; Bullwinkle, an astute student of relativity in spite of his cartoon upbringing, is at rest in the primed frame. The figures also indicate events A and B that occur at the following spacetime coordinates as measured in our unprimed frame and in Bullwinkle’s primed frame:

Event	Unprimed	Primed
A	(xA, tA)	( x ' A , t ' A )
B	(xB, tB)	( x ' B, t ' B)

In our frame, event A occurs before event B, with temporal separation ∆t = t_B − t_A = 1.00 µs and spatial separation ∆x = x_B − x_A = 400 m. Let ∆t' be the temporal separation of the events according to Bullwinkle. (a) Find an expression for ∆t' in terms of the speed parameter ß(= v/c) and the given data. Graph ∆t' versus ß for the following two ranges of ß:

(b) 0 to 0.01 (v is low, from 0 to 0.01c)

(c) 0.1 to 1 (v is high, from 0.1c to the limit c)

(d) At what value of ß is ∆t' = 0? For what range of ß is the sequence of events A and B according to Bullwinkle (e) the same as ours and (f) the reverse of ours? (g) Can event A cause event B, or vice versa? Explain.

Figure 37-25 Problem 21, 22, 60, and 61.