PHYSICS LETTERS B Spacetime quantization i duced by classical gravity

We propose spacetime uncertainty relations motivated by Heisenberg's uncertainty principle and by Einstein's theory of classical gravity. Quantum spacetime is described by a non-commutative algebra whose commutation relations do imply our uncertainty relations. We comment on the classical limit and on the first steps towards QPT over QST. 1. Limitations on the precision of localization in spacetime have appeared in the recent literature as con-sequences of different approaches to quantum gravity [ 1-3] or of some mathematical setup [4]. We propose a converse approach, where operationally motivated, though heuristically established, spacetime uncertainty relations are taken as the basis for motivating a novel mathematical model of quantum spacetime. The quan-tum nature of our model manifests itself in commuta-tion relations which are postulated on the basis of the following criteria: (a) They should imply our spacetime uncertainty relations. (b) They should be Poincar ~ covariant. (c) The commutators should vanish in the large scale limit. In other words our philosophy is that the quantum deviation of spacetime from its classical structure should be a consequence of the basic principles under-lying quantum mechanics and general relativity (point (a) ). Moreover those deviations should manifest themselves only at the Planck scale, whilst the larg