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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 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) |
|
B | (xB, tB) |
|
In our frame, event A occurs before event B, with temporal separation ∆t = tB − tA = 1.00 µs and spatial separation ∆x = xB − xA = 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.
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