  We discuss some effects induced by quantum field fluctuations on mass,
inertia and gravitation. Recalling the problem raised by vacuum field
fluctuations with respect to inertia and gravitation, we show that vacuum
energy differences, such as Casimir energy, do contribute to inertia. Mass
behaves as a quantum observable and in particular possesses quantum
fluctuations. We show that the compatibility of the quantum nature of mass with
gravitation can be ensured by conformal symmetries, which allow one to
formulate a quantum version of the equivalence principle. Finally, we consider
some corrections to the coupling between metric fields and energy-momentum
tensors induced by radiative corrections. Newton gravitation constant is
replaced by two different running coupling constants in the sectors of
traceless and traced tensors. There result metric extensions of general
relativity, which can be characterized by modified Ricci curvatures or by two
gravitation potentials. The corresponding phenomenological framework extends
the usual Parametrized Post-Newtonian one, with the ability to remain
compatible with classical tests of gravity while accounting for new features,
such as Pioneer like anomalies or anomalous light deflection.
