  The environment on the Moon has numerous features that make it interesting
not only for the study of astrophysical phenomena, but also elementary particle
physics. In fact, vacuum conditions, low gravity, and exposure to a relatively
intense irradiation of cosmic protons covering a large energy spectrum, make
the lunar environment attractive for a wide range of particle physics
experiments otherwise unworkable on Earth. We suggest one such experiment
measuring the difference between the amount of CP violation as measured on the
surface of the Earth and on the surface of the Moon, which could indicate
quantum gravitational effects
