Question

Two events are observed by inertial observer Stampy to occur a spatial distance of 15 c·s apart with the spatial coordinate of the second larger than the spatial coordinate of the first. Stampy also determines that the second event occurred 17 s after the first. According to inertial observer Philip moving along Stampy’s +x axis at unknown velocity v, the second event occurs 10 s after the first. (1 c·s = 1 light-second = unit of distance.)

a) Given Philip measures the spatial coordinate of the second event to be larger than the first, determine v.

b) How far apart spatially (in c·s) do the two events occur according to Philip?

c) Does there exist an inertial reference frame v < c in which the second event can occur before the first? Briefly explain in one sentence at most.
d) Inertial observer Kenny observes the proper time between the two events. How fast along Stampy’s +x axis does Kenny move?

(Note: Each part of this question can be done independently of any other. In part a, depending on how you solve it, you might obtain two answers as solutions of a quadratic, but one of them is extraneous, because it violates the premise in part a. If you are careful, you can avoid the quadratic at the outset, but it requires you to solve part b first.)

Answer 1