  Multi-messenger astronomy provides us with the possibility of discovering
phenomenological signatures of quantum-gravity effects. This should be of
paramount importance in the pursuit of an elusive quantum theory for the
gravitational interactions. Here we discuss feasible explorations within the
effective field theory treatment of general relativity. By exploring current
techniques borrowed from modern amplitude methods, we calculate leading quantum
corrections to the classical radiated momentum and spectral waveforms. The
lessons drawn from these low-energy results are that phenomenological
applications in gravitational-wave physics can be discussed in line with the
effective field theory approach. In turn, we also examine possible
phenomenological surveys from the perspective of a UV completion for quantum
gravity which employs the metric as the fundamental dynamical variable, namely
quadratic gravity. Being more specific, by resorting to the eikonal
approximation, we compute the leading-order time delay/advance in the
scattering of light by a heavy object and find a possible significant deviation
from the standard general-relativity prediction. This allows us to probe causal
uncertainty due to quantum fluctuations of the gravitational field as a genuine
prediction from Planck-scale physics.
