STRING THEORY, QUANTUM MECHANICS AND NONCOMMUTATIVE GEOMETRY: A NEW PERSPECTIVE ON THE GRAVITATIONAL DYNAMICS OF D0-BRANES

Abstract

We do not know the symmetries underlying string theory. Furthermore, there must exist an inherently quantum, and space–time independent, formulation of this theory. Independent of string theory, there should exist a description of quantum mechanics which does not refer to a classical space–time manifold. We propose such a formulation of quantum mechanics, based on noncommutative geometry. This description reduces to standard quantum mechanics, whenever an external classical space–time is available. However, near the Planck energy scale, self-gravity effects modify the Schrödinger 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 proposed here is actually the quantum gravitational dynamics of D0-branes, and that automorphism invariance is a symmetry of string theory.