photons - Selection rules in atomic physics . Why is $j' = 0$ to $j=0$ transition not allowed?

Consider the quantum numbers j (total angular momentum) and l (angular momentum) where j = l + s.
My notes state that:

Delta l can only be 1 or -1. Delta j can only equal 1 or zero, because the photon carries away one unit of angular momentum.

My question: A transition from j' = 0 to j = 0 is forbidden. Why is it this the case?