Upper bound of the time-space non-commutative parameter from gravitational quantum well experiment

Starting from a field theoretic description of the gravitational well problem in a canonical non-commutative spacetime, we have studied the effect of time-space non-commutativity in the gravitational well scenario. The corresponding first quantized theory reveals a spectrum with leading order perturbation term of non-commutative origin. GRANIT experimental data are used to estimate an upper bound on the time-space non-commutative parameter