Noncommutative unification of general relativity and quantum mechanics

We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity with those of quantum mechanics, and leads to correct "limiting cases" of both these physical theories. The noncommutative geometry of the fundamental level is nonlocal with no space and no time in the usual sense, which emerge only in the transition process to the commutative case. It is shown that because of the original nonlocality, quantum gravitational observables should be looked for among correlations of distant phenomena rather than among local effects. We compute the Einstein-Podolsky-Rosen effect; it can be regarded as a remnant or a "shadow" of the noncommutative regime of the fundamental level. A toy model is computed predicting the value of the "cosmological constant" (in the quantum sector) which vanishes when going to the standard spacetime physics.