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Problem 2.7

10 November, 2015 - 10:28
Naively, we would imagine that if a spaceship traveling at u=3/4 of the speed of light was to shoot a missile in the forward direction at v=3/4 of the speed of light (relative to the ship), then the missile would be traveling at u+v=3/2 of the speed of light. However, Einstein's theory of relativity tells us that this is too good to be true, because nothing can go faster than light. In fact, the relativistic equation for combining velocities in this way is not u+v, but rather (u+v)/(1+uv). In ordinary, everyday life, we never travel at speeds anywhere near the speed of light. Show that the nonrelativistic result is recovered in the case where both u and v are infinitesimal. 

Solutions for chapter 2