Quantum mechanics without spacetime: a case for noncommutative geometry
| dc.creator | Singh, T. P. | |
| dc.date | 2005-10-09 | |
| dc.date.accessioned | 2026-07-07T11:04:22Z | |
| dc.date.available | 2026-07-07T11:04:22Z | |
| dc.description | Quantum 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.description | 35 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.identifier | https://arxiv.org/abs/gr-qc/0510042 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0510042 | |
| dc.identifier | Bulg.J.Phys.33:217,2006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/188869 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Physics | |
| dc.title | Quantum mechanics without spacetime: a case for noncommutative geometry | |
| dc.type | text |