COW test of the weak equivalence principle: A low-energy window to look into the noncommutative structure of space-time?

We construct the quantum mechanical model of the COW experiment assuming that the underlying space time has a granular structure, described by a canonical noncommutative algebra of coordinates x^μ. The time-space sector of the algebra is shown to add a mass-dependent contribution to the gravitational acceleration felt by neutron deBrogli waves measured in a COW experiment. This makes time-space noncommutativity a potential candidate for an apparent violation of WEP even if the ratio of the inertial mass m_i and gravitational mass m_g is a universal constant. The latest experimental result based on COW principle is shown to place an upper-bound several orders of magnitude stronger than the existing one on the time-space noncommutative parameter. We argue that the evidence of NC structure of space-time may be found if the COW-type experiment can be repeated with several particle species.