Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / Section A / A10 / Solution

For photons emitted back to back in the measurement frame, their total invariant mass obeys $m^2{c}^4=(E_1+E_2{)}^2-(E_1-E_2{)}^2=4E_1{E}_2$. ThusThe parent's total laboratory energy is consequently about $160.2\mathrm{GeV}$, exceeding its rest energy. The measured-frame opposite-directions condition is essential: opposite directions only in the parent's rest frame would hold automatically and would not determine the second laboratory energy by itself.