  Classifying consistent effective field theories for the gravitational
interaction has recently been the subject of intense research. Demanding the
absence of causality violation in high energy graviton scattering processes has
led to a hierarchy of constraints on higher derivative terms in the Lagrangian.
Most of these constraints have relied on analysis that is performed in general
relativistic backgrounds, as opposed to a generic solution to the equations of
motion which are perturbed by higher curvature operators. Hence, these
constraints are necessary but may not be sufficient to ensure that the theory
is consistent. In this context, we explore the so-called CEMZ causality
constraints on Quadratic Gravity in a space of shock wave solutions beyond GR.
We show that the Shapiro time delay experienced by a graviton is
polarization-independent and positive, regardless of the strength of the
gravitational couplings. Our analysis shows that as far as the causality
constraints are concerned, albeit inequivalent to General Relativity due to
additional propagating modes, Quadratic Gravity is causal as per as the
diagnostic proposed by CEMZ.
