  We investigate the particle-antiparticle symmetry of the gravitationally
coupled Dirac equation, both on the basis of the gravitational central-field
problem and in general curved space-time backgrounds. First, we investigate the
central-field problem with the help of a Foldy-Wouthuysen transformation. This
disentangles the particle from the antiparticle solutions, and leads to a
"matching relation" of the inertial and the gravitational mass, which is valid
for both particles as well as antiparticles. Second, we supplement this
derivation by a general investigation of the behavior of the gravitationally
coupled Dirac equation under the discrete symmetry of charge conjugation, which
is tantamount to a particle -> antiparticle transformation. Limitations of the
Einstein equivalence principle due to quantum fluctuations are discussed. In
quantum mechanics, the question of where and when in the Universe an experiment
is being performed, can only be answered up to the limitations implied by
Heisenberg's Uncertainty Principle, questioning an assumption made in the
original formulation of the Einstein equivalence principle. Furthermore, at
some level of accuracy, it becomes impossible to separate non-gravitational
from gravitational experiments, leading to further limitations.
