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

TL;DR

This paper proposes a noncommutative geometric formulation of quantum mechanics that is spacetime-independent and reduces to standard quantum mechanics, providing insights into quantum gravity and D0-brane dynamics.

Contribution

It introduces a novel noncommutative geometric approach to quantum mechanics that applies at Planck scales and links to D0-brane quantum gravity.

Findings

Noncommutative quantum dynamics matches D0-brane behavior.

Near Planck scale, Schrödinger equation becomes nonlinear.

Automorphism invariance is identified as a symmetry of string theory.

Abstract

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.