Quantum mechanics without spacetime: a case for noncommutative geometry

dc.creatorSingh, T. P.
dc.date2005-10-09
dc.date.accessioned2026-07-07T11:04:22Z
dc.date.available2026-07-07T11:04:22Z
dc.descriptionQuantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such classical matter fields, quantum mechanics should be formulated without reference to a classical time. If such a new formulation exists, it follows as a consequence that standard linear quantum mechanics is a limiting case of an underlying non-linear quantum theory. A possible approach to the new formulation is through the use of noncommuting spacetime coordinates in noncommutative differential geometry. Here, the non-linear theory is described by a non-linear Schrodinger equation which belongs to the Doebner-Goldin class of equations, discovered some years ago. This mass-dependent non-linearity is significant when particle masses are comparable to Planck mass, and negligible otherwise. Such a non-linearity is in principle detectable through experimental tests of quantum mechanics for mesoscopic systems, and is a valuable empirical probe of theories of quantum gravity. We also briefly remark on the possible connection our approach could have with loop quantum gravity and string theory.
dc.description35 pages, based on an invited talk given at QTS-4 [Fourth International Conference on Quantum Theory and Symmetries], Varna, Bulgaria, 15-21 August, 2005
dc.identifierhttps://arxiv.org/abs/gr-qc/0510042
dc.identifierhttp://arxiv.org/abs/gr-qc/0510042
dc.identifierBulg.J.Phys.33:217,2006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/188869
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titleQuantum mechanics without spacetime: a case for noncommutative geometry
dc.typetext

Files

Collections