String theory, quantum mechanics and noncommutative geometry: a new perspective on the gravitational dynamics of D0-branes

T. P. Singh

Published 2006-05-11Version 1

We do not know the symmetries underlying string theory. Furthermore, there must exist an inherently quantum, and spacetime independent, formulation of this theory. Independent of string theory, there should exist a description of quantum mechanics which does not refer to a classical spacetime manifold. We propose such a formulation of quantum mechanics, based on noncommutative geometry. This description reduces to standard quantum mechanics, whenever an external classical spacetime is available. However, near the Planck energy scale, self-gravity effects modify the Schrodinger equation to the non-linear Doebner-Goldin equation. Remarkably, this non-linear equation also arises in the quantum dynamics of D0-branes. This suggests that the noncommutative quantum dynamics introduced here is actually the quantum gravitational dynamics of D0-branes, and that automorphism invariance is a symmetry of string theory.