Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-05-11
Int.J.Mod.Phys.D15:2153-2158,2006
Physics
High Energy Physics
High Energy Physics - Theory
6 pages. This essay received an honorable mention in the Gravity Research Foundation Essay Competition, 2006
Scientific paper
10.1142/S021827180600973X
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.
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