Space-time: Commutative or noncommutative ?

Abstract: Noncommutativity of the spacetime coordinates has been explored in several contexts, mostly associated to phenomena at the Planck length scale. However, approaching this question through deformation theory and the principle of stability of physical theories, one concludes that the scales of noncommutativity of the coordinates and noncommutativity of the generators of translations are independent. This suggests that the scale of the spacetime coordinates noncommutativity could be larger than the Planck length. This paper attempts to explore the experimental perspectives to settle this question, either on the lab or by measurements of phenomena of cosmological origin.