  We consider a thought experiment where the preparation of a macroscopically
massive or charged particle in a quantum superposition and the associated
dynamics of a distant test particle apparently allow for superluminal
communication. We give a solution to the paradox which is based on the
following fundamental principle: any local experiment, discriminating a
coherent superposition from an incoherent statistical mixture, necessarily
requires a minimum time proportional to the mass (or charge) of the system. For
a charged particle, we consider two examples of such experiments, and show that
they are both consistent with the previous limitation. In the first, the
measurement requires to accelerate the charge, that can entangle with the
emitted photons. In the second, the limitation can be ascribed to the quantum
vacuum fluctuations of the electromagnetic field. On the other hand, when
applied to massive particles our result provides an indirect evidence for the
existence of gravitational vacuum fluctuations and for the possibility of
entangling a particle with quantum gravitational radiation.
