  We propose a new test of local realism based on correlation measurements of
continuum valued functions of positions and momenta, known as modular
variables. The Wigner representation of these observables are bounded in phase
space, and therefore, the associated inequality holds for any state described
by a non-negative Wigner function. This agrees with Bell's remark that positive
Wigner functions, serving as a valid probability distribution over local
(hidden) phase space coordinates, do not reveal non-locality. We construct a
class of entangled states resulting in a violation of the inequality, and thus
truly demonstrate non-locality in phase space. The states can be realized
through grating techniques in space-like separated interferometric setups. The
non-locality is verified from the spatial correlation data, collected from the
screens.
