  Standard Quantum Physics states that the outcome of measurements for some
distant entangled subsystems are instantaneously statistically correlated,
whatever their mutual distance. This correlation presents itself as if there
were a correlation at a distance with infinite speed. It is expressed by the
Bell Theorem. It has been experimentally verified over distances up to 18 km
with a time resolution of a few picosecond, which can be translated into an
apparent effective correlation speed larger than 10^7 c. The purpose of the
present White Paper is to discuss the scientific interest and the feasibility
to extend the correlation distance up to the Earth-Moon distance, i.e. 2 10^4
times larger than in present experiments. We are thus led to propose to install
on the Moon a polarimter and a high performance photon detector with a high
temporal resolution. Such an exploratory experiment would provide new tests of
Quantum Physics and could perhaps discriminate between standard Quantum Physics
and for instance the Bohmian theory.
