2006/05/11 by T. P. Singh, T. P. SINGH · 1 citation
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1142/s021827180600973x
published as Int.J.Mod.Phys.D15:2153-2158,2006 · 6 pages. This essay received an honorable mention in the Gravity Research Foundation Essay Competition, 2006
arxiv created 2006/05/11 · openalex publication_date 2006/12/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.