Quantum tests of the foundations of general relativity

A new test theory for describing tests of fundamental principles of special and general relativity is presented. Using a generalized Pauli equation which may be based on a generalized Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes-Drever-type experiments or by atom interferometry. it is proposed that an atom interferometric test of local position invariance will give a three orders of magnitude improvement over existing estimates.