  In this note we discuss the relation between the constraints imposed by
causality in the bulk of $AdS$ and the condition of positivity of the energy
measured in ideal calorimeters in a collider experiment in the dual CFT. We
first extend the analysis in the literature and recover all bounds imposed by
causality of the boundary theory in the bulk dynamics for all polarizations of
the graviton and the gauge boson field. These results translate to specific
bounds for the ratio of central charges $\frac{a}{c}$ in the dual CFT, already
found by analyzing the energy one point function. Then, we generalize this
discussion and we study shock wave backgrounds in which we make manifest the
relation between causality in the bulk and the three point function in the dual
field theory. We remark that particular care has to be given to the
exponentiation procedure of the three point function when solving the classical
equations of motion in the higher gravity theory, as it is not clear that every
theory will present causality problems. Finally, we present a field theoretic
argument explaining the positivity of energy condition in any UV complete QFT.
