  The stability of the nuclear matter system with respect to density
fluctuations is examined exploring in detail the pole structure of the
electro-nuclear response functions. Making extensive use of the method of
dispersion integrals we calculate the full polarization propagator not only for
real energies in the spacelike and timelike regime but also in the whole
complex energy plane. The latter proved to be necessary in order to identify
unphysical causality violating poles which are the consequence of a neglection
of vacuum polarization. On the contrary it is shown that Dirac sea effects
stabilize the nuclear matter system shifting the unphysical pole from the upper
energy plane back to the real axis. The exchange of strength between these real
timelike collective excitations and the spacelike energy regime is shown to
lead to a reduction of the quasielastic peak as it is seen in electron
scattering experiments. Neglecting vacuum polarization one also obtains a
reduction of the quasielastic peak but in this case the strength is partly
shifted to the causality violating pole mentioned above which consequently
cannot be considered as a physical reliable result. Our investigation of the
response function in the energy region above the threshold of nucleon
anti-nucleon production leads to another remarkable result. Treating the
nucleons as point-like Dirac particles we show that for any isospin independent
NN-interaction RPA-correlations provide a reduction of the production amplitude
for $p\bar p$-pairs by a factor 2.
