In molecular dynamics (MD) simulations, the continuum description of electrostatic interactions has been based in most cases on the static response of the dielectric continuum. In this work, a time-dependent reaction field expression including stochastic and friction terms is derived in analogy to the generalized Langevin equation involving hydrodynamic interactions. Simulations of water using the extended simple-point charge model have been performed under different boundary conditions. The effects of a time-dependent treatment of the reaction field are demonstrated by comparing the results to those of MD simulations using a static, instantaneous reaction field and of MD simulations employing the Ewald sum. It is shown for the first time that the straight cutoff approach not only leads to a disruption of the time, but also of the spatial correlation of the dipole moment.