Equivalence Principle for Antiparticles and its Limitations

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.