Chapter 2, Problem 109E

From $\text{p}={\gamma }_{u}m\text{u}$ (i.e., $p_x={\gamma }_{u}m{u}_x$ , $p_y={\gamma }_{u}m{u}_y$ , and $p_z={\gamma }_{u}m{u}_z$ ), the relativistic velocity transformation (2−20), and the identity ${\gamma }_{u^{\prime }}=\left(1-u_{x}v/c^2\right){\gamma }_v{\gamma }_u$ , show that ${p^{\prime }}_y=p_y$ and ${p^{\prime }}_z=p_{z^{\prime }}$ .