Relativistic reversal of events figures a and b show the (usual) situation in which a primed reference frame passes an unprimed reference frame, in the common positive direction of the x and x' axes, at a constant relative velocity of magnitude y. 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 space time coordinates as measured in our unprimed frame and in Bullwinkle's primed frame: In our frame, event A occurs before event B, with temporal separation Δt = tB – tA = 1.00 ps and spatial separation Δt = xB – xA = 400 m. Let Δt be the temporal separation of the events according to Bullwinkle.

(a) Find an expression for Δt in terms of the speed parameter β (= v/c) and the given data. Graph A/' versus B for the following two ranges of β:

(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)