Relativistic reversal of events. Figures 37-25a and b show

Chapter , Problem 21

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Relativistic reversal of events. Figures 37-25a 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 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 Bullwinkles primed frame: Event Unprimed Primed A (xA, tA) B (xB, tB) In our frame, event A occurs before event B, with temporal separation 2t ! tB & tA ! 1.00 ms and spatial separation 2x ! xB & xA ! 400 m. Let be the temporal separation of the events according to Bullwinkle. (a) Find an expression for in terms of the speed parameter b (! v/c) and the given data. Graph 2t# versus b for the following two ranges of b: (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 b is 2t# ! 0? For what range of b 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.