This crystal can split light particles

+Physics Girl 3:11 How? Even if you assume that the crystal and the whole setup is infinitely massive compared to the energy of a photon so that the energy lost in recoil is zero and there is no other energy loss, you can't send the 'daughter photons' in two different directions.
Because for a photon E = p*c (p = magnitude of a photon's momentum). So If the 'mother photon' had momentum (p1,0,0) and energy p1*c, the daughters have total x-momentum = p1 and energy p1*c. So the daughters leaving along x axis would satisfy the energy and momentum conservation.  But if they also have (say) any y-momentum then the daughters will have more combined energy than the mother, violating the energy conservation. 
And if the crystal recoils, matters become even worse.