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## Homework Statement

Consider an inertial frame ##S## with coordinates ##x^{\mu}=(t,x,y,z)##, and a frame ##S'## with coordinates ##x^{\mu'}## related to ##S## by a boost with velocity parameter ##v## along the ##y##-axis. Imagine we have a wall at rest in ##S'##, lying along the line ##x'=-y'##. From the point of view of ##S##, what is the relationship between the incident angle of a ball hitting the wall (travelling in the ##x##-##y## plane) and the reflected angle? What about the velocity before and after?

## Homework Equations

## The Attempt at a Solution

From the point of view of ##S'##, the incident angle equals the reflected angle.

The frame ##S'## travels parallel to the ##y##-axis of the frame ##S##. Therefore, ##y'=-x' \implies \gamma\ y = - x##.

Therefore, from the point of view of the ##S## frame, the wall has a gentler slope (i.e., slope of smaller magnitude).

Will the trajectories also change their directions in the ##S## frame?